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ABCD abſurd alſo Altitude Angle ABC Baſe BC becauſe biſect C O R O Caſe Center conft conſequently Cylinder demonſtrated deſcribed Diameter draw the right drawn EFGH equal Angles equiangular equilateral Equimultiples Exceſs firſt fore given right Line gles Gnomon greater Hence inſcribe leſs leſſer likewiſe Line CD Magnitudes manifeſt Number oppoſite Paral parallel Parallelepip Parallelepipedons Parallelogram perpend perpendicular Point Polyhedron poſſible Priſm Probl Propoſition Pyramid Q. E. D. P R O Ratio Rečiangle Rećtang right Angles right Line AB right Line AC right-lined Figure ſaid ſame Altitude ſame Multiple ſay ſecond Segment ſhall be equal ſimilar ſince ſolid ſome Sphere Square ſtanding ſubtending ſuch ſuppoſe theſe thoſe tiple Triangle ABC Uſe Whence whole whoſe
Side 29 - 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 143 - Equal triangles which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional : And triangles which have one angle in the one equal to one angle in the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Side 31 - ABD, is equal* to two right angles, «13. 1. therefore all the interior, together with all the exterior angles of the figure, are equal to twice as many right angles as there are sides of the figure; that is, by the foregoing corollary, they are equal to all the interior angles of the figure, together with four right angles; therefore all the exterior angles are equal to four right angles.
Side 25 - If two right-angled triangles have their hypotenuses equal, and one side of the one equal to one side of the other, the triangles are congruent.
Side 29 - The three angles of any triangle taken together are equal to the three angles of any other triangle taken together. From whence it follows, 2.
Side 217 - ... to one of the consequents, so are all the antecedents to all the consequents ; [V. 12] hence the whole polyhedral solid in the sphere about A as centre has to the whole polyhedral solid in the other sphere the ratio triplicate of that which AB has to the radius of the other sphere, that is, of that which the diameter BD has to the diameter of the other sphere. QED This proposition is of great length and therefore requires summarising in order to make it easier to grasp. Moreover there are some...
Side 9 - That a straight line may be drawn from any point to any other point. 2. That a straight line may be produced to any length in a straight line.
Side 217 - And as one antecedent is to its confequent, fo are all the antecedents to all the confequents. Wherefore the whole folid polyhedron in the greater fphere has to the whole folid polyhedron in the other, the triplicate ratio of that which AB...