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 Artificial
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added altitude angle ABC angle BAC arch baſe becauſe biſect Book XI circle circle ABCD circumference common cone contained cylinder deſcribed diameter difference divided double draw drawn EFGH equal equiangular equimultiples fall fame fides firſt folid fore four fourth given given right line greater half inſcribed join leſs likewiſe magnitudes meet oppoſite parallel parallelogram perpendicular plain polygon priſms produced Prop proportional proved pyramid ratio rectangle remaining right angles right lined figure ſame multiple ſame reaſon Secant ſegment ſides ſimilar Sine ſolid ſphere ſquare taken Tang tangent THEO theſe third touch triangle triangle ABC Wherefore whole
Page 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.
Page 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.
Page 91 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Page 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.
Page 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.
Page 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.
Page 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.
Page 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...
Page 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.