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 10,000, and Tables of Sines, Tangents, and Secants, Natural and Artificialauthor, and sold, 1776 - 264 sider |
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Resultater 1-5 af 45
Side 149
... Secant , and Cofec . Cofecant . a 3. 3 . b 15 , 40 C IS . 3 . SCHOLIU M. * Because the triangles CED , CBG , ( fig . for the definitions , ) are fimilar , CE : ED :: CB : BG , by alter . CE : CB :: ED : BG , i . e . Cof . : R :: Sine ...
... Secant , and Cofec . Cofecant . a 3. 3 . b 15 , 40 C IS . 3 . SCHOLIU M. * Because the triangles CED , CBG , ( fig . for the definitions , ) are fimilar , CE : ED :: CB : BG , by alter . CE : CB :: ED : BG , i . e . Cof . : R :: Sine ...
Side 150
... Secant . And , because the triangles CDF , CED , CBG , and CHI , are fimi- lar , CE ED CF : FD ; but CEFD ; therefore ED = CF4 ; therefore CE is the fine of the angle CDE = DCF . Again , EC : D :: CB : BG ; altern . EC : CB : ED : BG ...
... Secant . And , because the triangles CDF , CED , CBG , and CHI , are fimi- lar , CE ED CF : FD ; but CEFD ; therefore ED = CF4 ; therefore CE is the fine of the angle CDE = DCF . Again , EC : D :: CB : BG ; altern . EC : CB : ED : BG ...
Side 17
... which are Annexed Plain and Spherical Trigonometry, Tables of Logarithms from 1 to 10,000, and Tables of Sin Euclid George Douglas. A T A B LE O F Artificial SINES , TANGENTS , and SECANTS . C Sine . M o Degree . Tang . Secant .
... which are Annexed Plain and Spherical Trigonometry, Tables of Logarithms from 1 to 10,000, and Tables of Sin Euclid George Douglas. A T A B LE O F Artificial SINES , TANGENTS , and SECANTS . C Sine . M o Degree . Tang . Secant .
Side 18
... Secant . O 2.0000000 10.000000 0.0000000 Infinite . 10.0000000 Infinite . 65 I 2 7647561 3 9408473 7.0657860 4637261 9.9999999 | 6.4637261 13.5362739 9999999 7647562 2352438 9999998 9408475 0591525 9999997 7.0657863 12.9342137 0000000 ...
... Secant . O 2.0000000 10.000000 0.0000000 Infinite . 10.0000000 Infinite . 65 I 2 7647561 3 9408473 7.0657860 4637261 9.9999999 | 6.4637261 13.5362739 9999999 7647562 2352438 9999998 9408475 0591525 9999997 7.0657863 12.9342137 0000000 ...
Side 19
... Secant . 08.241855319-9999338 8.2419215 11.7580785 10.0000662 ( 11.7581447 60 I 2490332 9999316 2491015 0000684 7508985 7509668 59 2 2560943 9999294 2561649 7438351 0000706 7439057 58 3 2630424 9999271 2631153 7368847 0000729 7369576 57 ...
... Secant . 08.241855319-9999338 8.2419215 11.7580785 10.0000662 ( 11.7581447 60 I 2490332 9999316 2491015 0000684 7508985 7509668 59 2 2560943 9999294 2561649 7438351 0000706 7439057 58 3 2630424 9999271 2631153 7368847 0000729 7369576 57 ...
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The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Ingen forhåndsvisning - 2015 |
Almindelige termer og sætninger
ABCM angle ABC angle BAC arch bafe bafe BC baſe becauſe bifected 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 reaſon fecond fegment femicircle fhall fides fimilar folid angle folid parallelopipedons fome fore fphere fquare of AC fubtending given right line greater infcribed join lefs leſs likewife magnitudes parallel parallelogram perpendicular plain paffing polygon polyhedron prifms PROP pyramid rectangle right angles right line AB right lined figure Secant Sine Tang tangent thefe THEOR theſe triangle ABC triplicate ratio Wherefore whofe bafe whoſe
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Side 80 - 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 72 - F, equal to them in number, be taken two and two in the fame ratio, and if their analogy be perturbate, 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 91 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Side x - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles, these straight lines being continually produced, shall at length meet upon that side on which are the angles which are less than two right angles.
Side 54 - Let ABC be the given circle, and D the given straight line, not greater than the diameter of the circle. It is required to place in the circle ABC a straight line equal to D.
Side 9 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 13 - 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 69 - 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...
Side 91 - 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 80 - ... 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.