The Elements of Euclid,: In which the Propositions are Demonstrated in a New and Shorter Manner Than in Former Translations, and the Arrangement of Many of Them Altered, to which are Annexed Plain and Spherical Trigonometry, Tables of Logarithms from 1 to 10000, and Tables of Sines, Tangents, and Secants, Both Natural and ArtificialJ. Murray, no. 32. Fleetstreet; and C. Elliot, Parliament-square, Edinburgh., 1776 - 264 σελίδες |
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Σελίδα viii
... taken another demonftra- tion in place of that used in the 2d propofition , which I thought as mathematical as that used either by Commandine or Simpson , and much shorter . To the 8th prop . I have added , " that only two " equal lines ...
... taken another demonftra- tion in place of that used in the 2d propofition , which I thought as mathematical as that used either by Commandine or Simpson , and much shorter . To the 8th prop . I have added , " that only two " equal lines ...
Σελίδα x
... taken up in barely demonftrating the propofitions , may be employed in pointing out their particular beauties , the accura- cy of the reasoning , their use in the affairs of life , and their ap- plication to the fciences , which will be ...
... taken up in barely demonftrating the propofitions , may be employed in pointing out their particular beauties , the accura- cy of the reasoning , their use in the affairs of life , and their ap- plication to the fciences , which will be ...
Σελίδα xi
... taken ; for , if folid fi- gures , bounded by an equal number of equal and fimilar planes , are not equal and fimilar , but under this limitation , then prop . 15. Book V. must not be univerfally true , which I fuppofe will ́not eafily ...
... taken ; for , if folid fi- gures , bounded by an equal number of equal and fimilar planes , are not equal and fimilar , but under this limitation , then prop . 15. Book V. must not be univerfally true , which I fuppofe will ́not eafily ...
Σελίδα 3
... . III . If from equal things equal things be taken , the remainders will be equal . IV1 If to unequal things equal things are added , the whole will be unequal , V. I £ Book I. BOOK I V. I from unequal things equal parts are OF EUCLID .
... . III . If from equal things equal things be taken , the remainders will be equal . IV1 If to unequal things equal things are added , the whole will be unequal , V. I £ Book I. BOOK I V. I from unequal things equal parts are OF EUCLID .
Σελίδα 12
... taken , are , together , lefs than two right angles . The Let ABC be the triangle , any two angles in it are less than two right angles . For , produce BC both ways to D , E ; then , becaufe the out- ward angle ACD is greater than ABC ...
... taken , are , together , lefs than two right angles . The Let ABC be the triangle , any two angles in it are less than two right angles . For , produce BC both ways to D , E ; then , becaufe the out- ward angle ACD is greater than ABC ...
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The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2022 |
The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2022 |
The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCM angle ABC angle BAC arch bafe baſe becauſe bifect Book XI circle ABCD circle EFGH circumference cofine common fection cone contained cylinder defcribe DEFH diameter draw drawn equal angles equal to AC equiangular equilateral equimultiples fame altitude fame multiple fame plain fame proportion fame reafon fecond fegment femicircle fides fimilar folid angle fome fore fquare of AC fubtending given right line greater infcribed join lefs leſs Let ABC magnitudes oppofite parallel parallelogram perpendicular plain angles plain paffing polygon prifms Prop pyramid rectangle right angles right line AB right lined figure Secant Sine ſphere ſquare Tang tangent thefe THEOR theſe triangle ABC triplicate ratio Wherefore whofe ΙΟ
Δημοφιλή αποσπάσματα
Σελίδα 93 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG ; the...
Σελίδα 78 - ... viz. as A is to B, fo is E to F, and B to C as D to E ; and if the firft A be greater than the third C, then the fourth D will be greater than the fixth F ; if equal, equal ; and, if lefs, lefs.
Σελίδα 88 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 99 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Σελίδα 19 - From this it is manifest that if one angle of a triangle be equal to the other two it is a right angle, because the angle adjacent to it is equal to the same two ; (i.
Σελίδα 75 - Let AB be the fame multiple of C, that DE is of F : C is to F, as AB to DE. Becaufe AB is the fame multiple of C that DE is of F ; there are as many magnitudes in AB equal to C, as there are in DE equal...
Σελίδα 88 - ... reciprocally proportional, are equal to one another. Let AB, BC be equal parallelograms which have the angles at B equal, and let the sides DB, BE be placed in the same straight line ; wherefore also FB, BG are in one straight line (2.
Σελίδα 99 - BGC: for the same reason, whatever multiple the circumference EN is of the circumference EF, the same multiple is the angle EHN of the angle EHF: and if the circumference BL be equal to the circumference EN, the angle BGL is also equal to the angle EHN ; (in.
Σελίδα 106 - ... but BD, BE, which are in that plane, do each of them meet AB ; therefore each of the angles ABD, ABE is a right angle ; for the same reason, each of the angles CDB, CDE is a right angle: and because AB is equal to DE, and BD...
Σελίδα 73 - RATIOS that are the same to the same ratio, are the same to one another. Let A be to B as C is to D ; and as C to D, so let E be to F ; A is to B, as E to F.