« ΠροηγούμενηΣυνέχεια »
Join BA and Ac. Then, because ABD is a triangle whose the rectangle contained by the whole line thus produced, and the
For the same reason the squares of B C and cd are together
Therefore, adding equals to equals, the squares of A B, BD, CD,
But the square of BD is equal to four times the square of B E
Therefore the squares of A B, BC, CD, and D A are together equal
Again, because eaC is a triangle, of which the base Ac is
It is required to produce a B so that the rectangle contained by
From the point B in the straight line A B draw BH at right
Bisect A B in the point G and join G 1.
Produce a B to meet the circumference in 1. Then the rect-
Because Bu is equal to CD (Cons.), therefore the square of
B H is equal to the square of on, that is the square CDEF.
Again, because a Bo is a right angled triangle having the right
But the square of G H has been above shown to be equal to the square of G i. Therefore (I. Ax. 1) the square of a L is equal to the squares of G B and Bh together.
But the square of G L is equal to the square of a B together with the rectangle A L, L B (II. 6).
Therefore (I. Ax. 1) the squares of a B and RI are together
From each of these equals take away the common square of a B,
then (I. Ax. 3) the rectangle A L, L B is equal to the square of
Bisect AB in G (I. 10). From a draw ou at right angles to
ANSWERS TO CORRESPONDENTS.
JOHN BURROUGH: The POPULAR EDUCATOR has been published in the
United States. We cannot promise to act upon your suggestion.
any lessons in Spanish, but we should be glad if it were possible.
G. LAKEMAN is referred to the two volumes of the “Historical Edu-
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EDUCATOR.” We have no wish to engage in theological controversy.
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SIMPLICITAS (Wemyss, Fireshire) has solved the first thirty-two of the Therefore the square of u m is equal to the square of GM second Centenary of Algebraical Problems; D. HORNBY (Drittiold) the first together with the rectangle A M, MB.
filty-five, with the exception of Nos. 7, 12, 35, 37, 39, 43, and 51; GEORGE
WILD (Dalton-on-Tees) the whole of the second portion from No. 23 to 70;
and Q'Q. (Fenchurch-street) the first thirty-two, except Nos. 16, 23, 26,
28, 30, and 31, besides Nos, 40, 41, and 51 of the second portion.
D. HORNBY (Driffield): The following is George Wild's solution of Pro-
5 9 Days Days
: : 10 : 18
square of u g is equal to the square CD EF (Cons.).
Prop. E. Problem. To produce a given straight line, so that • The above five exercises were solved by J. H. EASTWOOD (Middleton).
Let z be the number of days in which B could do this part of the work
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JOHN CASSELL, LA BELLE SAUVAGE YARD, LUDGATE HILL.
THE PRESENT Series of the Popular EDUCATOR is now completed. It was our intention to have closed it with a Supplement to Volume V., consisting of some 200 pages. But the difficulty of completing so many subjects in that limited space, together with urgent appeals from numerous Readers and Correspondents, induced us to postpone its termination till the completion of another Volume, uniformn with the five preceding. This will explain the continuity of the paging from the commencement of the Fifth Volume to the close of the work. The appearance of uniformity will be greatly preserved by having the entire Series bound in three double volumes.
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XXVIII. La vierge aus ruines. Sections I., II., III., IV.,
V., with exercises, etc.
L'emploi du temps, with exercises, etc.
roi et la jeune fille ; Sections I., II., with ex
ercises, etc. XXXI. Sections III., IV., with exercises etc. La
charité; Section I., with exercises, etc. XXXII. Section II., with exercises. Eudoxie ; Sections
I. II., with exercises, etc.......
en péril, with exercises, etc.
LESSONS IN ALGEBRA.
Evolution; Reduction of Radical Quantities 416
Radical Quantities; Multiplication of Radical
Radical Quantities; Evolution of Radical
tion of Equations by Evolution; Adfected
Method for Completing the Square ; Demon-
591 XXVIII. Geometrical Proportion and Progression. 624 XXIX. Problems in Geometrical Progression; Evolu. tion of Compound Quantities
tion of Decimals; Contractions in Multiplica-
tions; Contractions in Division of Decimals 486 XXXII. Periodical, or Circulating Decimal; Reduction
of Circulating Decimals; Addition of Circu-
510 XXXIII. Percentage; Commission; Brokerage; and Stocks
544 XXXIV. Interest; Compound Interest.
674 XXXV. Discount; Bank Discount; Insurance ;
606 XXXVI. Life Insurance ; Profit and Loss
640 XXXVII. Analysis
654 XX. Edward Gibbon
670 XXI. Oliver Goldsmith....
684 XXII. William Cowper
699 XXIII. Felicia Dorothea Hemans........
714 XXIV. Sarah Margaret Fuller
730 XXV. Laura Bridgman.......:
747 XXVI. Catharine Maria Sedgwick
762 XXVII. Mrs. Trollope XXVIII. Mary Russell Mitford
795 XXIX. Lydia Huntley Sigourney.
497 VI. Diphthongs; Nasal Vowel Sounds; Nasal Diphthongal Sounds
524 VII. Liquids; General Rule for Pronouncing and Reading French
with exercises, etc. Le chien du Louvre,
455 XXVII. Section II., with exercises
LESSONS IN GEOLOGY.
» Lithological Character of the
651 LXI. Old Red Sandstone, or the Devonian Forma
tiun; Lithological Character of the Devonian;
421 XLVIII. Invariable Words
437 XLIX. Syntax; Preliminary Explanations; Subject; Predicate; Agreement; Government
450 L. The Parts of a Simple Sentence considered separately; their Agreement.
465 LI. Voices of the Verb...
479 LII. Tenses of the Verb..
499 LIII. Moods
515 LIV. Enlargement of Simple Sentences.
546 LV. Attributives; the Demonstrative Pronouns; the Article
576 LVI.. Attributive Words with Substantive Import;
Enlargement of the Predicate.......... 603 LVII.
the Single Accusative .. 641 LVIII. The Predicate with a Double Accusative. 674 LIX. Import and Use of the Dative .
701 LX. Import and Use of the Genitive....
736 LXI. Syntax of the Prepositions
76+ LXII. Interrogative and Imperative Sentences 1799
LESSONS IN ITALIAN.
449, 467 XXXVII. Irregular Verbs ending in 'ere short;"Verbs ending in cere
501 XXXIX. Verbs ending in dere”.
530 XL. Verbs ending in urre, contracted from cere; Verbs ending in gere
561 XLI. Vebs ending in ggere ; Verbs ending in gliere ; Verbs ending in guere.......
593 XLII. Verbs ending in lore; Verbs ending in mere; Verbs ending in pere ...
627 XLIII. Verbs ending in orre; Verbs ending in rere;
Verbs ending in tere; Verbs ending in arre;
659 XLIV. Table of Terminations of the Verbs in isco 676 XLV., XLVI.
688, 703 xLvii.' Impersonal Verbs; Participle : Adrerb
722 XLVIII. Preposition ; Conjunction; Interjection
739 XLIX. Syntax : Of Articles
of Nouns, Adjectives, Comparatives and Superlatives, Numerals..
Cor Personal, Possessive, Demonstralire, Relative, and Interrogative Pronouns.. 786 LU.
Of Indefinite Pronouns; of Verbs 801 LIII. Qi Participles, Adverbs, and Conjunctions... 813