# 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 Artificial

J. Murray, no. 32. Fleetstreet; and C. Elliot, Parliament-square, Edinburgh., 1776 - 264 СЕКъДЕР

### пЕЯИЕВЭЛЕМА

 еМЭТГТА 1 5 еМЭТГТА 2 13 еМЭТГТА 3 14 еМЭТГТА 4 24 еМЭТГТА 5 24 еМЭТГТА 6 24 еМЭТГТА 7 26 еМЭТГТА 8 34
 еМЭТГТА 17 79 еМЭТГТА 18 100 еМЭТГТА 19 100 еМЭТГТА 20 101 еМЭТГТА 21 128 еМЭТГТА 22 128 еМЭТГТА 23 128 еМЭТГТА 24 146

 еМЭТГТА 9 43 еМЭТГТА 10 54 еМЭТГТА 11 54 еМЭТГТА 12 55 еМЭТГТА 13 63 еМЭТГТА 14 65 еМЭТГТА 15 66 еМЭТГТА 16 78
 еМЭТГТА 25 148 еМЭТГТА 26 154 еМЭТГТА 27 154 еМЭТГТА 28 8 еМЭТГТА 29 15 еМЭТГТА 30 18 еМЭТГТА 31 44

### дГЛОЖИКч АПОСПэСЛАТА

сЕКъДА 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...
сЕКъДА 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.
сЕКъДА 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.
сЕКъДА 99 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
сЕКъДА 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.
сЕКъДА 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...
сЕКъДА 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.
сЕКъДА 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.
сЕКъДА 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...
сЕКъДА 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.