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ABCD abſurd alſo be equal alſo be greater alſo equal angle ABc angle AcB angle BAc angle DEF becauſe biſe&t caſe centre chord circle ABc circumference Conſ conſequently Conſt conſtruction demonſtration deſcribe diameter diſtance draw equal baſes equiangular equimultiples Euclid fides fince firſt given right line inſcribed interſe&ts join the points leſs Let ABC magnitudes muſt obſerved oppoſite angles outward angle parallelogram paſs paſſes perpendicular polygon priſm Prop proportional propoſition Q. E. D. P R O remaining angle right angles ſaid ſame baſe ſame manner ſame multiple ſame plane ſame ratio ScholIUM ſe&tion ſecond ſegment ſemicircle ſhall ſhewn ſide Bc ſimilar ſince the angles ſolid ſome ſpace ſquares of Ac ſtand ſuch ſum T H E o R. E. M. tangent theſe thoſe lines triangle ABc uſe whence whoſe
Side 164 - 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 213 - Lemma, if from the greater of two unequal magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there shall at length remain a magnitude less than the least of the proposed magnitudes.
Side 115 - In a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF. Draw the straight line GAH touching the circle in the point A (III. 17), and at the point A, in the straight line AH, make the angle HAG equal to the angle DEF (I.
Side 16 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. LET ab be the given straight line, which may be produced to any length both ways, and let c be a point without it. It is required to draw a straight line perpendicular to ab from the point c.
Side 247 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Side 100 - To bisect a given arc, that is, to divide it into two equal parts. Let ADB be the given arc : it is required to bisect it.
Side 3 - AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will be unequal.