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LESSONS IN GEOGRAPHY.No. VI. GEOGRAPHICAL DISCOVERIES OF THE SIXTEENTH AND SEVENTEENTH CENTURIES. Tax new information gained by the old world, through the appearance of Franklin in Europe from the East, of what we discovery of America and the voyage of Vasco de Gama, re- would such a frightful and dangerous passage be to the merquired a long period for its proper regulation and systematic cantile interests of the world ? Surely it would still be better arrangement. The ignorance which still prevailed among the to pursue the ordinary route to India, either by sea or land, ablest navigators and geographers, at the end of the fifteenth than to run the danger and risk of losing ships, property, and century, was such that, when Christopher Columbus, in his men, by sailing through floating mountains of ice, unknown third voyage, discovered continental America, the violence of rocks, and uninhabited and in hospitable coasts. the billows, and the agitation of the sea at the mouth of the The voyage of Willoughby in 1553, although it ended in a Orinoco, led him to believe that he was in the highest part of sad shipwreck on the eastern coast of Lapland, added to geothe globe, and consequently, in the regions of paradise ! But graphical knowledge, by the discovery of Nova Zembla. Frothe discovery of the new world revived and reinvigorated bisher, under Queen Elizabeth, was more fortunate; his three the desire for voyages to the north, and set them on a better voyages, performed between 1576 and 1578, ended in some footing. It appears, indeed, that previous to his grand dis- discoveries, among which were the straits which bear his covery, Columbus had himself performed a voyage in the name, situated between Hudson's Straits and Cumberland northern seas, and had even visited Iceland. This voyage, Straits. John Davis, in the same reign, in his exploratory WESTERN HEMLSPHERE


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according to a note of the event found in his own handwriting, voyages performed in 1585, 1586, and 1587, threw a clearer took place in 1467.

light on the geography of the circumpolar regions of the John and Sebastian Cabot, who were employed in the ex. north. In 1596 the Dutch discovered Spitzbergen ; and pedition by Henry VII. of England, discovered the island of eleven years afterwards it was rediscovered by Hudson, who Newfoundland, and sailed along a considerable extent of the performed four voyages, from 1607 to 1611, in order to find the coast of North America. France, desirous of having her share passage to India either across the pole itself or to the north. of the spoil, fitted out an expedition under J. Cartier, who west. In the fourth, he discovered the bay which bears his sailed from Dieppe in 1534; discovered Canada, and took pos- name. In the following year Thomas Button, penetrating session of it in the name of his government. The grand object into this northern Mediterranean, reached the mouth of the of these voyages in the northern seas, was the discovery of a river Nelson. William Baffin enjoyed still greater success. In north-west passage to India. The infatuated question of a his second exploratory voyage, in 1616, he successively discommunication between the two great oceans at the north, covered and gave name to the following places in the arctic occupied the minds of geographers and navigators at that regions :—Cape Dudley Digges, in latitude 76° 35' N.; the period, as much as it has done in the present day. How bay of Wolstenholme; the bay of Whales, in latitude 77° singular that this infatuation still occupies the public mind! 30' N.; the island of Hackluyt; the bay of Sir Thomas Smith, Bren on the supposition that such a passage really existed, and in latitude 78° N.; also the Carey Islands, the bay of Alderman had been actually discovered, and put in evidence by the re-Jones, and Lancaster Sound. In this expedition, he explored VOL. I.



the bay which has immortalised his name, and determined the as to the realities of our colonial possessions. Even gold itself geographical position of a great number of points.

may become a drug; and how sad that state of society would During the sixteenth century, while discoveries were multi- be, when this most precious of metals, having made all equally plied and expeditions became fruitful and productive, georich, would fail to purchase that human labour, from which graphical science still remained in its infantile state, and as our comforts flow! yet received little advantage from their progress. Light was There has been also the fable of the kingdom of Paititi, a breaking in upon all sides, but this science was immersed in sort of counterpart of El Dorado, another garden of ihe darkness. A glance at the fantastical maps which preceded the Hesperides, where inexhaustible treasures awaited the happy glorious era of the Reformation, will show how profound was the mortal sufficiently well instructed to follow the track. This ignorance of the geographers of that period. In our last lesson, kingdom or empire was supposed to be situated in the fertile a specimen of one of the-e maps was given in the fac-simile plains of the Maranon, and to have been founded by the of the map of Africa belonging to the pilot of Christopher Incas of Peru, whose descendants knew how to conceal them Columbus. In such maps of the world, the principal cities are from the view of the Spaniards by powerful enchantments! denoted by little houses or churches roughly sketched; Jeru. By degrees this myth was embellished with a thousand wonders, salem occupies the centre of the globe : paradise is surrounded and the Catholic missionaries themselves contributed not a with its impenetrable enclosure of verdant foliage; and the little to propagate the conviction that this imaginary kingdom geographical illustrations are the most whinsical that can be was a realiiy. This state of things continued even in the imagined. The winds are represented by fabulous divinities, second half of the seventeenth century. The close of the middle as sitting all round the world upon leathern bottler, whose sides ages, therefore, had its mythical or fabulous geography, notwiththey are pressing to force out the air ; Western Africa is made to standing the real and ultimate progress made by the voyages terminate at Cape Nun, then at Cape Bojador; the celebrated of discovery. True science had not yet made its appearance, statue of the Canaries is seen flourishing his club at the top The fifteenth century having closed with the two greatest of a high tower; the coasts of the adjacent continent are geographical events of modern times, the discovery of the lengthened in proportion to the discoveries of the Portuguese ; New World, and the periplus of the African continent, the Abyssinia figures with its Prester John, having on his head a sixteenth century beheld the extension and success of European brilliant miire; the other kingdoms of Africa are denoted by enterprise in distant seas. The Pacific Ocean, which Magellan their kings in costumes, enriched with gold and silver em- had opened up to the fleets of Christendom, were navigated broidery; this continent so long unknown, is represented as and explored by daring mariners. Soarez discovered the peopled with strange animals and black men ; there are groups Maldive Islands; another Portuguese, the Moluccas or Spice of giraffes and elephants; Portuguese camps are indicated by Islands; Villalobos, a group now supposed to make part of the coloured tents; and light cavalry, splendidly caparisoned, are Philippine Islands ; Juan Fernandez, the small island that making the tour of this mysterious continent. In short, these bears his name, and celebrated as the foundation of the history specimens of chartographical art, are the faithful expression of Robinson Crusoe. To the latter, also, has been ascribed the of the science of the middle ages. The pilot's map, already discovery of New Zealand. In 1567 Alvaro de Mendana alluded to, will furnish the reader with exaniples of the pre- tirst landed on the Solomon Isles, the isle of Santa Cruz, and ceding details. Behold the contrast in the map of the world others. Nearly thirty years later, the same navigator discovered which accompanies this lesson! We have inserted his map the Marquesas, and the Archipelago, which was afterwards thus early in our progress, that it may be useful for reference; called by Carteret Queen Charlotte's Islands. Francis it will be fully described in a future lesson.

Drake; the Dutchman Van Noort ; Quiros, who discovered The period preceding the Reformation, was the era of Tahiti, and the Archipelago of the New Hebrides (the Great legendary and popular tales, and geography had its fabulous Cyclades of Bougainville); Torres, who discovered New age as well as its antiquity; only the fantastic notions of the Guinea, and the strait which separates this large island from middle ages were less marked by ingenuity and variety. Australia,-all began to clear up the navigation of the Pacific or Prester John has been mentioned. This was one of their most South Sea. In the interval, Sebald de Weert, fellow-navigawidely-spread myths. The name of this personage first ap- tor with Van Noort, had recognised the Malouines cr Falkland peared about the middle of the twelfth century. It was the Islands, discovered by John Davis. Two of his countrymen, general and popular belief that there existed a pontifical Lemaire and Schouten, discovered in 1615, part of the island prince called John, who governed vast countries situated beyond of Terra del Fuego, and Cape Horn, which forms the southern Armenia and Persia. It was asserted that he professed that extremity of the American continent. A new passage was form of Christianity called Nestorianism. Ere long he was thenceforward open to navigators bound for the Pacific Ocean, transported to Abyssinia, where he ruled during three or four who were desirous of avoiding the difficulties and storms centuries! He was as rich as he was powerful, and as which were to be dreaded in the straits of Magellan. The formidable to his enemies, as he was dear to his subjects. In honour of having first landed on New Holland (Australia) is Asia or in Africa, there was always a formidable monarch, generally attributed to Dirk Hartog, who attached to the part dwelling in a world of prodigies, over which he reigned as of this continent, which he had discovered, the name of the omnipotent master!

vessel he commanded, by calling it Endracht's land ; Zeacher, The vain tradition of El Dorado was no less believed at the in 1618; Edels, in 1619; De Nuyts, in 1627; and after these period under review. This fiction, which travelled to America De Witt, Carpenter, and Pelsart completed this grand disunder the name which has given celebrity to it, in the first covery. half of the sixteenth century, was applied to a country, that It is not positively known whether the Spanish and the previously existed only in the imagination of the inhabitants Portuguese had not visited the coasts of Australia nearly a of Europe. Although its true name is lost, it was at last century before the Dutch, as two chartographical documents placed in the new world, in the country of Santa Fé, in those of that date would lead us to believe. Neither is it more cer. regions of South America watered by the mighty streams oftain that the Portuguese Menezes and the Spaniard Saavedra the Amazon, and which were scarcely known to Europeans. I had discovered New Guinea, the one in 1527, and the other in El Dorado, this name sufficiently indicates the nature of the the following year. The memorable voyage of Abel Tasman imaginary country to which it was applied. It was the country produced rapid and striking progress in the geography of of riches; there, were to be seen cities glittering with gold; Oceanica, or Australasia and Polynesia. This able navi. there, so common was this metal, that it was used even in the yator, sailing from Batavia in 1642, discovered Van Diemen's most common household utensils. How unfortunate for ages, Land, otherwise called after him Tasmania, The periplus of were the adventures in search of this goiden dream! How Australia was then compleied, and the assurance was guined many victims have been deceived by this dangerous tradition! that this continent did not extend indetinitely towards the Is this El Dorado to be at last realist-d in our own day? Are south pole. Shortly after, the expedition landed on New California and Australia to give actual existence to the fables Zealand; then it discovered the Friendly Islands, and that of of the middle sgus? Modern appliances are great; chemistry | Tongataboo. Lastly, after a successful expedition of nine and geology have done wonders ; and human industry has en months, at the end of which it visited New Guinea, and dis. countered what at the beginning of the present century were covered several islands to the north of it and of the island of deemed impossibilities. But le: us not be too sanguine now, New Britain, the Dutch refitted their vessels in the port of


Batavia, the capital of Java. It was only in 1665 that the Prester John ? What was the nature of the fiction of El Dorado ? name of Nora Hollandia, or New Holland, was given to the and of that of Païtiti? Name some of the discoverers in Australasia. western part of Australia by a decree of the States-General of and Polynesia. What English names occur at this period as disthe parent country.

coverers? What French names? Who first set foot on Australia? In 1700 Dampier, at this time celebrated for his buccaneer who gave it the name of New Holland? Who discovered Van

What was it at first called ? (piratical) expeditions, discovered some new islands to the the world at the beginning of the 18th century? Who discovered

Who sailed round north of New Guinea, and Papuasia, -that is, small islands the narrow straits between Asia and America ? What ditficult contiguous to New Guinea, which was also called Papua. question did this discovery solve ? Who was Bougainville ? and Wood Rogers şailed sound the world in three years and three what discoveries did he make? months, and encouraged by his successful expedition, the maritime powers proceeded to attempt similar enterprises, hitherto considered as extremely dangerous. Towards the end of the preceding century, France had also made expeditions into the

LESSONS IN FRENCH.-No. XIX. Southern Ocean. Her first vessel which appeared in the Pacific Ocean, was commanded by one Lafeuillade ; but the

By Professor Louis FASQUELLE, LL.D. voyage, which took place in 1667, produced no new discovery. The discoveries of the Russians in the north of Asia must be

SECTION XL. noticed, At the beginning of the seventeenth century, they

THE PAST INDEFINITE. [$ 121.) knew nothing of the coasts of Siberia beyond the Yenisei. War and conquests laid open to the emperors the way to this 1. The past indefinite is composed of the present of the in. immense region. In the space of less than a century, the dicative of one of the auxiliary verbs, avoir and être [$45 (8)], whole of northern Asia, from the frontiers of China to the and the participle past of a verb. See the different paradigms Frozen Ocean, was reduced under the crown of Russia. Geo- pf verbs, § 47 and following sections. graphy was benefited by this annexation, which gave to the

J'ai parlé, je suis arrivé. I have spoken, I have arrived. Russians new facilities for performing useful explorations in these inhospitable countries. In 1728 Behring alone made the

2. The past indefinite is used to express an action entirely important discovery of the strait which separates Asia from completed, but performed at a time of which a part is not yet America, and rendered the peopling of the new world no longer elapsed, or at time entirely past, but not specified. [$ 121 a question of difficulty or doubt.

(1) (2)] : The northern circumpolar regions had not been the theatre J'ai vu votre père ce matin. I have seen your father this morning, of any important expedition, from that of Baffin, above Je ne vous ai pas encore parlé. I have not yet spoken to you. mentioned, until the middle of the eighteenth century. The The past indefinite may also be used, when the time is speciera of scientific expeditions was now begun. Geography, so fied [§ 121 (3)]:long retarded in her progress to perfection, proceeded with a

Je lui ai écrit la semaine dernière. I wrote to him last week. a sure and rapid step. This was the most brilliant period of

Je lui ai envoyé une lettre le mois I sent him a letter yesterday. the history of navigation from the time of the great discoveries of the sixteenth century. It was particularly remarkable for the positive character of its results. Bougainville, who had 4. In this tense and in other compound tenses, the adverb is gained renown in the wars of Canada, anticipated that which generally placed between the auxiliary verb and the participle he gained as a navigator, by an expedition to the Malouine or ($ 136 (3)] :Falkland Islands where he went to found a French colony in

Vous nous avez souvent parlé. You have often spoken to us. 1764. The circumnavigation of the world by commodore Je ne l'ai pas encore vu.

I have not yet seen him Byron, also begun in the same year, produced very important results; and so did the voyages of Wallis and Carteret, in

5. The adverbs aujourd'hui, to-day; demain, to-morrow; hier, clearing up some practical questions relating to the geography long adverbs generally, do not come between the auxiliary

yesterday ; polysyllabic adverbs of manner ending in ment, and of Oceanica. Carteret, in particular, determined the geograr verb and the participle, but follow Rule 1. Sect. 33. See § 136 phical positions (that is, the latitudes and longitudes) of

(5) :several islands in the direction of New Britain ; his vessel

Vous avez lu dernièrement. You read lately. having been the first Euglish man-of-war which had touched at the island of Celebes. Three years after his first voyage, 6. The unipersonal verb y avoir (Sect. 32, R. 3, 4), placed in 1767, Bougainville undertook his grand expedition to cir- before a word expressing time, corresponds with the English cumnavigate the globe. After a short stay in the river La word, ago :Piata, he was detained in the straits of Magellan no less

J'ai reçu une lettre, il y a huit jours. I received a letter eight days ago. than a period of fifty-two days. He then entered the South

Vous avez acheté une maison, il y a You bought a house a year ago. Sea, and discovered the islands of Pomotou, which he called the Dangerous Archipelago. He then entered the chief port of Tahiti; his transactions with the inhabitants of New

Cythera were not only pacific but amicable. He next visited
the Navigator's island, or Samoa, touched at Papua or New Vos neveux nous ont parlé. Your nephew spoke to us.
Guinea, discovered to the east of it an archipelago which he Nous avons parlé à votre père. We spoke to your father.

Has the tailor made my coat ! called Louisiade, several of the Admiralty Isles, and another Le tailleur a-t-il fait mon habit ?

Le boulanger a inis son chapeau. The baker has put on his hat. called by his own name near Solomon Isles. In the same direction he discovered several other islands of less import- Votre frère a dit quelque chose.

Le cordonnier a ôté ses souliers, The shoemaker has taken his shoes off.

Your brother said something. ance, which had been seen by other navigators; and having Votre sæur qu'a-t-elle dit?

What did your sister say! visited New Ireland, discovered by Carteret, he arrived at N'avez vous rien dit à mon cousin ? Hare you told my cousin nothing ? Batavia; whence, he sailed to Europe by the Cape of Good Je ne lui ai rien dit.

I hare told him nothing. Hope. This expedition was well received in France and in Je ne l'ai jamais rencontré.

I have never met him. Europe; it had made several important discoveries, and had Je ne leur ai jamais parlé.

I never spoke to them. been marked with interesting episodes which were related Qu'avez vous fait aujourd'hui ? What have you done to-day?

We did not work yesterday. with spirit and talent; and created a still greater desire for Hier, nous n'avons pas travaillé. circumnavigating expeditions.

Leur en avez vous souvent parlé ? Have you often spoken to them about QUESTIONS ON THE PRECEDING LESSON.

Je leur en ai souvent parlé.

I hare often spoken to them about it. Who discovered America? Had this discovery any immediato Je ne le leur ai pas encore dit. I have not yet said any thing to them effect on géographical sciente ? What was the object of the voyages to the northern regions in the 17th century? What discoveries N'avez vous pas assez écrit ? Have you not written enough? did F:obisher, Davis, and Baffin make at this period? What I m'a écrit, il y a lougtemps. He wrote to me a long time ago. appearance did the maps of the world then present? Who was Il nous a répondu il y a un mois. He reptied to us a month ago.


un an.


about it.


agrees in gender and number with its direct object or régime

direct [82 (2), § 42 (4)], when that object precedes it Avocat, m. barrister; Gargon, m boy ; Mis, from mettre, put on; (§ 134 (4) Cela, ceci, that, this; Hier, yesterday ; Plant-er, 1. to plant ;

Journée, f, day:
Dit, from dire, said ;

Poirier, m. pear-tree;
Les dames que nous avons vues.

The ladies whom we have seen.
Soulier, m. shoe;

Les lettres que nous avons lues. Etadi-er, 1. to study; Lu, from lire, read;

The letters which we have read. Gart, m. glove; Ministre, m. minister; Vu, from voir, seen. 8. When the régime direct or objective (accusative) follows

1. Qui vous a dit cela ? 2. L'avocat me l'a dit. 3. Lui the participle, no agreement takes place ($ 134 (5)]: avez vous parlé de cette affaire ? 4. Je ne lui en ai pas encore Avez vous vu les dames ?

Have you seen the ladies 1 parlé. 5. L'avez vous vu dernièrement? 6. Je l'ai vu il y a Avons nous lu les lettres ?

Have we read the letters ? quelques jours. 7. N'avez vous pas écrit hier? 8. Nous avons lu et écrit toute la journée. (Sect. 25 (9).] ,9. N'avez vous indirect object (dative or ablative) [$ 2 (3), § 42 (5)]:

9. A participle past never agrees with its régime indirect, or pas ôté vos gants et vos souliers ? 10. Je n'ai pas ôté mes

The ladies to whom we have spoken. gants, mais j'ai ôté mon chapeau ? 11. Le tailleur n'a-t-il pas Les dames à qui nous avons parlé. mis son chapeau ? 12. Oui, Monsieur, il a mis son chapeau. 10. The participle past used adjectively, that is, without an 13. Qu'avez vous fait à ce petit garçon? 14. Je ne lui ai rien auxiliary verb follows the rule of the adjective ($ 66 (3), $ fait. 15. Ne lui avez avous point dit que je suis ici? 16. Je 134 (1)) :ne le lui ai pas encore dit. 17. Qu'avez vous étudié ce matin?

Des livres bien imprimés. Well printed books. 18. Nous avons étudié nos leçons et nous avons lu nos livres.

11. The participle, preceded by the relative pronoun en, re19. Le jardinier du ministre a-t-il plante le poirier: 20. Il l'a planté il y a plus de huit jours. 21. Avez vous acheté un mains invariable, although the en should relate to a feminine habit de drap noir? 22. J'en ai acheté un. 23. L'avez vous

or plural noun [$ 135 (7)]:porté aujourd'hui ? 24. Je ne l'ai pas encore porté. 25. Nous Avez vous apporté des plumes ? Have you brought pens ? avons mis nos souliers et nos bas ce matin.

J'en ai apporté.

I have brought some.

12. The presence of en does not, however, prevent the agreeEXERCISE 80.

ment of the participle, when it is preceded by a direct regimen 1. Have you studied to-day? 2. We have no time to study, [$ 135 (7)):we have read a page. 3. Have you not written to my brother ? Les plumes que j'en ai apportées. The pens which I have brought from is. 4. I have not yet written to him. 5. Has not the German written to my mother? 6. He has not yet written to her. 7. Have you told (à) my mother that I have taken (pris) this

RESUMÉ OF EXAMPLES. book? 8. I have not yet seen your mother. 9. What have Vos sœurs ont elles écrit?

Have your sisters written? you done this morning : 10. We have done nothing. 11. Elles n'ont pas encore écrit. They have not yet written, Have you taken off your coat? 12. I have not taken off my Les lettres que nous avons écrites. The letters which we have written. coat, it is too cold. 13. Has the bookseller written to your Avez vous écrit vos lettres ? Have you written your letters ? brother? 14. He wrote to him a long time ago. 15. Did he Je les ai lues, je les ai écrites. I have read them, I have written them. write to him a month ago 16. He wrote to him more than a

Les avez vous apportées ?

Have you brought them!
Je ne les ai pas apportées.

Fhave not brought them. year ago. 17. Have you planted a pear-tree? 18. We have

Have you called those ladies ? planted several. 19. Is it too cold

to (pour) plant trees? 20. Avez vous appelé ces dames ?
Je ne les ai pas appelées.

I have not called them.
It is too warm,

21. What has the gardener done to your Qui avez vous vu ce matin ? Whom have you seen this morning ? little boy? 22. He has done nothing to him. 23. Has any Nous avons vu ces demoiselles. We have seen those young ladies. one done any thing to him? 24. No one has done anything to Nous les avons vues.

We have seen them. him. 25. Is anything the matter with him? 26. Nothing is Nous ne leur avons pas parlé. We have not spoken to them. the matter with him. 27. Has your father put on his black Avez vous des livres reliés ? Have you bound books ? hat? 28. No, Sir, he has not put on his black hat. 29. What J'a. des livres broches.

I have unbound (stitched, in paper has your brother said: 30. He has said nothing. 31. Has

covers,) books. your sister told you that ? 32. She told it me. 33. Did you Avez vous acheté des pommes ? Have you bought apples !

I hare bought some. not work yesterday? 34. We did not work yesterday, we had j'en ai acheté. nothing to do. 35. Your little boy has done nothing to-day, Noms les en avons persuadés.

We have bought some.

We have persuaded them of it.


Achet-er, 1. to buy. (8 49 Donn-er 1, to give; Gard er, 1. to keep; 1. The past participle, which in French forms a part of Apport-er, 1. to bring;


Dit, from dire, 4 ir. Gravure, f. engraving; said;

Oubli-er, 1. to forget , every compound tense [§ 45 (8)], is susceptible of changes in Appel-er, 1.to call. (8 49 Entend-re, 4. to hear; Rec-evoir, 3. to receive , its termination.


Examin-er, 1. to ex- Reli-er, 1. to bind ; 2. The student will find in the table of the terminations of Broch-er, 1. to stitch; amine;

Revenus, m. p. income, the regular verbs [$ 60), the different changes which the past Bourse, f. purse; Exprès, on purpose ; Tasse, f. cup; participle of these verbs undergoes. The feminine terminations Cass-er, 1. to break; Fleur, f. flower; Vu, from voir, 3 ir, seen. of the past participle of the irregular verbs, will be found in Commission, f. errand. the alphabetical table, $ 62. 3. The last letter of the feminine termination is always an

1. Nous avez vous apporté nos habits ? 2. Nous ne les

avons pas encore apportés. 3. Les avez vous oubliés? 4. Nous e mute.

ne les avons pas oubliés, mais nous n'avons pas eu le temps de 4. The plural of a past participle not ending with an s, is les apporter. 5. Pourquoi n'avez vous pas appelé les marformed by the addition of that letter to the singular, masculine chands? 6. Je les ai appelés, mais ils ne m'ont pas entenda. or feminine, 5. The participle past, accompanied by the auxiliary verb 9. N'avez vous pas vu les jolies fleurs que j'ai apportées : 10.

7. Avez vous entendu cette musique : 8. Je l'ai entendue. avoir, never agrees with the nominative or subject ($ 134 (3)]:- Je les ai vues; à qui les avez vous données ? 11. Je ne les ai Les demoiselles ont chanté,

The young ladies sang.

données à personne, je les ai gardées pour vous. 12. Avez Ces messieurs ont lu toute la journée. Those gentlemen read the whole day. vous bien examiré ces gravures ? 13. Je les ai bien examinées.

6. The participle past, having être as its auxiliary verb, as- 14. Les avez vous achetées. 16. Je ne les ai point achetées. sumes in its termination the gender and number of the subject 16. N'avez vous point reçu vos revenus ? 17. Je ne les ai [§ 134 (2)] :

point encore reçus.

18.' La domestique a-t-elle cassé ces

tasses ? 19. Elles les a cassées. Ma fille est arrivée ce matin.

20. A-t-elle cassé des tasses Nos frères ne sont pas venus.

My daughter arrived this morning. exprès. 21. Elle n'en a pas ca ssé exprès. 22. Avez vous

Our brothers are not come. acheté des livres reliés ou brochés,. 23. J'ai acheté des livres 7. The participle, accompanied by the auxiliary verb avoir, reliés. 24. Nous avez vous dit au paroles ? 25. Nous vous

les avons dites, mais vous les avez oubliées. 26. Je n'ai pas called a line, and has no breadth. For, if it have any, this breadth oublié votre commission.

must be part either of the breadth of the superficies A B C D, or of

the superficies KBC L, or part of each of them. It is not part of EXERCISE 82.

the superficies KBCL; for, if this superficies be removed from 1. Have you seen my cups ? 2. I have not yet seen them. the superficies A B C D, the line B C, which is the boundary of the 3. Have you brought me my books! 4. I have not forgotten superficies A B C D, remains the same as it was; nor can the them, I have left them (laiss-er, 1.) at my brother's. 5. Has breadth that B C is supposed to have be a part of the superficies your mother called your sisters ? 6. She has not yet called ABCD; because, if this superficies be removed from the super. them. 7. Has the servant told you this news? (nouvelle.) 8. ficies KBCL, the line BC, which is the boundary of the super. She has told me this news. 9. She has told it me. 10. Have ficies KBC L, does nevertheless remain. Therefore the line BC you forgotten my errand? 11. We have not forgotten it, we has no breadth. And, because the line B C is in a superficies, and have forgotten your money. 12. Where have you left your that a superficies has no thickness, as was shown, therefore a line purse : 13. We left it at the merchant's. 14. Have you bought has neither breadth nor thickness, but only length. the beautiful (belles) engravings .which I saw at your book- The boundary of a line is called a point, or a point is the comsellers? 15. I have not seen them. 16. Has your mother mon boundary or extremity of two lines that are contiguous. Thus, bought them? 17. She has bought books, but she has bought if B be the extremity of the line A B, or the common extremity of no engravings. 18. Has that little girl broken my cups : 19. the two lines A B and KB, this extremity is called a point, and She has broken them on purpose. 20. Does that lady receive has no length. For, if it have any, this length must either be part her income every month 21. She receives it every six months. of the length of the line A B, or of the line K B. It is not a part 22. Is the house which you have bought large? 23. I have of the length of KB; for if the line K B be removed from the line bought no house. 24. Did you receive a letter from your A B, the point B, which is the extremity of the line A B, remains father yesterday? 25. I received a letter from him four days the same as it was; nor is it a part of the length of the line A B; ago. 26. Have you spoken to those ladies ? 27. I have spoken for, if the line A B be removed from the line KB, the point B, to them. 28. Have you given them flowers ? 29. I have which is the extremity of the line K B, does nevertheless remain. given them some (en) 30. Are the books which you have Therefore the point B has no length. And, because a point is in a bought bound? 31. No, Sir, they are in paper covers. 32. line, and that a line has no length, breadth, or thickness ; therefore Have you examined that house? 33. I have not examined it. a point has no length, breadth, or thickness. And in this manner 34. Your brother (en) has examined several (plusieurs). the definitions of a point, a line, and a superficies are to be under.


This explanation of Dr. Simson is so complete that nothing can

be added to it. He who does not understand in what sense the LESSONS IN GEOMETRY.-No. IX.

terms, point, line, superficies or surface, and solid are to be taken LECTURES ON EUCLID.

in the Greek Geometry, after what has been said above, must In our last lecture, we stopped just at the point when every one

be unacquainted with the meaning of the simple words that wished most anxiously to know what we had to say about a point;

are employed, or else deficient in the ordinary gift of human

intellect. we mean a geometrical point. Well, we have often given the sub

We shall not suppose that any of our readers are stance of Dr. Simson's explanation, when lecturing to a class sider further explanation of these terms unnecessary,

in either of these predicaments ; and therefore we shall con

We without book ; but here we must present our students with the ipsissima verba, the very words themselves written by that learned come now to consider the important definition of a straight

line. This Dr. Simson has not considered it requisite to explain, man. “ It is necessary to consider a solid, that is, a magnitude which withont justice. Of course, we take it as the Dr. has given it to

Yet great fault has been found with Euclid's definition, and not bas length, breadth, and thickness, in order to understand aright the definitions of a point, a line, and a superficies ; for all these us; for, to enter into the question of the meaning of the Greek arise from a solid and exist in it. The boundary, or boundaries, our chief object, and could not be expected to interest every reader.

terms, which he has translated, would lead us too far away from which contain a solid, are called superficies, * or the boundary The principal fault of the definition of a straight line is, that in the which is common to two solids which are contiguous (adjacent), or explanation, no very definite property of a straight line is involved. which divides one solid into two contiguous parts, is called

a super. The word evenly, on which it hinges, is in its application here, ncarly ficies. Thus, if BCGF be one of the boundaries which contain synonymous with straight ; and therefore the definition almost the solid A B C D E F GH,+ or which is the common boundary of this solid, and

amounts to this : a straight line is a straight line. Seeing this, it

has been declared, by some geometers, that the idea of a straight the solid B KLCFNMG, and is there. E

line is so simple and self-evident, that it is incapable of logical defore in the one, as well as in the other, solid;

finition. However this may be, all writers on geometry, and all it is called a superficies and has no thick

editors of Euclid, have considered it necessary to give some defininess. For, if it bave any, this thickness

tion of a straight line. Our esteemed friend Dr. Thomson, in his must either be a part of the thickness of

edition, adopts the definition given by Professor Playfair, as a subthe solid AG, or of the solid B M, or a

в к

stitute for Euclid's; viz., “ If two lines be such that they canpart of the thickness of each of them. It cannot be a part of the thickness of the solid B M; because if this them is called a straight line." This definition is manifestly im.

not coincide in two points without coinciding altogether, each of solid be removed from the solid AG, the superficies BCG F, the perfect, because two arcs of the same circle, are two lines such that boundary of the solid A G, remains still the same as it was.. Nor in a certain position they cannot coincide in two points without cocan it be a part of the thickness of the solid AG, because if this inciding altogether, and yet neither of them is a straight line. Dr. (thickness) be removed from the solid BM, the superficies Thomson felt this, and therefore in his notes, he added an explaBCGF, the boundary of the solid B M, does nevertheless remain. nation or illustration to the effect that it was necessary to consider Therefore the superficies has no thickness, but only length and the two lines in all positions, like two rulers placed alongside breadth.

each other, and made to turn round and round on their axes, or The boundary of a superficies is called a line, or a line is the lengthwise upon one another. In an edition referred to in our common boundary of two superficies that are contiguous, or which last lesson, an attempt is made to convey the idea of a straight divides one superficies into two contiguous parts. Thus, if B C be line in the following manner :-“If a perfectly flexible strizg one of the boundaries which contain the superficies A B C D, or be pulled by its extremities in opposite directions, it will aswhich is the common boundary of this superficies and of the super- sume, between the two points of tension, a certain position. ficies KBCL, which is contiguous to it, this boundary BC is Were we to speak without the rigorous exactitude of geometry we This is a Latin word of the fifth declension like res, and it is the same

should say that it formed a straight line. But upon consideration, both in the pominative singular and the nominative plural; this is also re- it is plain that the string has weight, and that its weight produces a tained in its English use; in the present case it is plural.

flexure in it, the convexity of which will be turned towards the The letters here which represent the solid are those at each of its eight surface of the earth. If we conceive the weight of the string to be corners, the line joining which would pass right through the middle of the extremely small, that flexure will be proportionably small; and if, solid.

by the process of abstraction, we conceive the string to bave no









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