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 71
Side viii
... likewife fo . The fame may be faid of the 36th and 38th ; nor is it lefs natural to prove it from half the parallelogram than to double the triangle , and then take its half . I cannot agree with Mr Simpson in leaving out the ...
... likewife fo . The fame may be faid of the 36th and 38th ; nor is it lefs natural to prove it from half the parallelogram than to double the triangle , and then take its half . I cannot agree with Mr Simpson in leaving out the ...
Side 6
... likewife equal to Cd : Which was required . I PRO P. IV . THEOREM . F there be two triangles having two fides of the one equal to two fides of the other , each to each ; and the angle contained by the two fides of the one , equal to the ...
... likewife equal to Cd : Which was required . I PRO P. IV . THEOREM . F there be two triangles having two fides of the one equal to two fides of the other , each to each ; and the angle contained by the two fides of the one , equal to the ...
Side 7
... likewife equal ; but the angles DEF , ABC , are b Ax . 1 . equal ; therefore the angles ABC , ACB , are likewife equal . Wherefore , & c . CORROLLARY . If any triangle is equilateral , it will likewife be equiangular . PRO P. VI . THE O ...
... likewife equal ; but the angles DEF , ABC , are b Ax . 1 . equal ; therefore the angles ABC , ACB , are likewife equal . Wherefore , & c . CORROLLARY . If any triangle is equilateral , it will likewife be equiangular . PRO P. VI . THE O ...
Side 9
... likewife equal : Therefore each of them & 8 . is a right angle , and FC perpendicular to AB . Which was Def . 10 required . T PRO P. XII . PRO B. O draw a right line perpendicular to a given indefinite right line from a given point out ...
... likewife equal : Therefore each of them & 8 . is a right angle , and FC perpendicular to AB . Which was Def . 10 required . T PRO P. XII . PRO B. O draw a right line perpendicular to a given indefinite right line from a given point out ...
Side 11
... likewife the angles CEB , AED , equal to one another . For , because the right line CE falls upon the right line AB , the angles AEC , CEB , are equal to two right angles . For the fame reason the angles AED , AEC , are equal to two ...
... likewife the angles CEB , AED , equal to one another . For , because the right line CE falls upon the right line AB , the angles AEC , CEB , are equal to two right angles . For the fame reason the angles AED , AEC , are equal to two ...
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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.