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 sider |
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Resultat 1-5 av 44
Side 149
... Secant , and Cofec . Cofecant . 2 3. 3 . b 15 , 4 C 15. 3 . SCHOLIU M. Because the triangles CED , CBG , ( fig . for the definitions , ) are fimilar , CE : ED :: CB : BG , by alter . CE : CB BG , i . e . Cos , : R ;; Sine : Tangent ...
... Secant , and Cofec . Cofecant . 2 3. 3 . b 15 , 4 C 15. 3 . SCHOLIU M. Because the triangles CED , CBG , ( fig . for the definitions , ) are fimilar , CE : ED :: CB : BG , by alter . CE : CB BG , i . e . Cos , : R ;; Sine : Tangent ...
Side 150
... Secant . And , because the triangles CDF , CED , CBG , and CHI , are fimi- lar , CE ED : CF : FD ; but CE = FD ; therefore ED = CF d ; therefore CE is the fine of the angle CDE = DCF . Again , EC : ÉD :: CB : BG ; altern . EC : CB : ED ...
... Secant . And , because the triangles CDF , CED , CBG , and CHI , are fimi- lar , CE ED : CF : FD ; but CE = FD ; therefore ED = CF d ; therefore CE is the fine of the angle CDE = DCF . Again , EC : ÉD :: CB : BG ; altern . EC : CB : ED ...
Side 18
... Secant. 1626960 9999995 1626964 6 2418771 9999993 2418778 7581222 ク 3088239 9999991 3088248 8 3668157 9999988 3668169 M I Sine . o Degree . Tang . 6.0000000 10.000000 0.0000000 Infinite . 637261 9.9999999 | 6.4637261 13.5362739 7647561 ...
... Secant. 1626960 9999995 1626964 6 2418771 9999993 2418778 7581222 ク 3088239 9999991 3088248 8 3668157 9999988 3668169 M I Sine . o Degree . Tang . 6.0000000 10.000000 0.0000000 Infinite . 637261 9.9999999 | 6.4637261 13.5362739 7647561 ...
Side 19
... Secant . } I 2490332 2 2560943 9999294 2561649 08.241855319.9999338 8.2419215 | 11.7580785 10.0000662 11.7581447 60 9999316 2491015 7508985 7438351 0000684 0000706 3 2630424 2631153 9999271 7368847 0000729 7509668 59 7439057 58 7369576 ...
... Secant . } I 2490332 2 2560943 9999294 2561649 08.241855319.9999338 8.2419215 | 11.7580785 10.0000662 11.7581447 60 9999316 2491015 7508985 7438351 0000684 0000706 3 2630424 2631153 9999271 7368847 0000729 7509668 59 7439057 58 7369576 ...
Side 20
... Secant . 08.54281929.9997354 8.5430838 | 11.456916210.0002646 | 11.4571808 60 I 5464 : 18 9997309 5466909 4533091 0002691 4535782 59 2 5499948 9997265 5502683 4497317 0002735 4500052 58 3 5535386 9997220 5538166 4461834 0002780 4464614 ...
... Secant . 08.54281929.9997354 8.5430838 | 11.456916210.0002646 | 11.4571808 60 I 5464 : 18 9997309 5466909 4533091 0002691 4535782 59 2 5499948 9997265 5502683 4497317 0002735 4500052 58 3 5535386 9997220 5538166 4461834 0002780 4464614 ...
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Vanlige uttrykk og setninger
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Populære avsnitt
Side 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...
Side 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.
Side 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.
Side 99 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Side 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.
Side 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...
Side 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.
Side 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.
Side 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...
Side 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.