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 páginas |
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Página iii
... Secants , both Natural and Artificial . B Y GEORGE DOUGL A S , Teacher of Mathematics in the Academy at Ayr . ** LOND DON : Printed for J. MURRAY , No. 32. Fleetfireet ; and C. ELLIOT , Parliament - fquare , Edinburgh . M. DCC.LXXVI ...
... Secants , both Natural and Artificial . B Y GEORGE DOUGL A S , Teacher of Mathematics in the Academy at Ayr . ** LOND DON : Printed for J. MURRAY , No. 32. Fleetfireet ; and C. ELLIOT , Parliament - fquare , Edinburgh . M. DCC.LXXVI ...
Página ix
... Secants , and verfed Sines , both natural and artificial ; and how to change Briggs's Logarithms to the Hyper- bolic , and vice versa , with examples of the above . To which are annexed TABLES of the Logarithms of Numbers , of Sines ...
... Secants , and verfed Sines , both natural and artificial ; and how to change Briggs's Logarithms to the Hyper- bolic , and vice versa , with examples of the above . To which are annexed TABLES of the Logarithms of Numbers , of Sines ...
Página 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 ...
Página 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 ...
Página 1
... SECANTS , the Radius 10,0000000 ; and to every Degree and Minute of the Quadrant , Num . Log . Num . Log . Num . Log . 5 1234 SO D∞ I 0.0000000 0.3010300 0.4771213 0.6020600 0.6989700 333 e cu cu cu cu 34 36 1.5314789 I.5440680 ...
... SECANTS , the Radius 10,0000000 ; and to every Degree and Minute of the Quadrant , Num . Log . Num . Log . Num . Log . 5 1234 SO D∞ I 0.0000000 0.3010300 0.4771213 0.6020600 0.6989700 333 e cu cu cu cu 34 36 1.5314789 I.5440680 ...
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The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Sin vista previa disponible - 2022 |
The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Sin vista previa disponible - 2022 |
The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Sin vista previa disponible - 2015 |
Términos y frases comunes
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Pasajes populares
Página 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...
Página 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.
Página 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.
Página 99 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Página 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.
Página 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...
Página 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.
Página 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.
Página 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...
Página 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.