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The Contents of the Fifth and Sixth Books of Euclid
Euclid,Micaiah John Muller Hill
Πλήρης προβολή - 1900
angles reciprocally proportional arc CD base BEFG BEHC bisected BLNO CÂD centre circle Commutative Law compartments congruent corresponding sides cross-ratio Definition draw duplicate ratio EFGH ENUNCIATION equal angles equimultiples EXAMPLE expressed by Fig Fifth Book four harmonic points greater Hence the scale hypotenuse integers kind mean proportional middle point multiples of G parallel to BC parallelogram ABCD point at infinity point of division PQRST Prop Proportion 66 PROPOSITION rA rB rA sB radical axis rAsC ratio compounded ratio of equality rect rectangle contained relative multiple scale required to prove respectively equal right angle rTsV second column segments side AC side corresponding similar figures similar triangles similarly described Sixth Book supplementary angles Theory of Relative three magnitudes triangle ABC triangle are respectively triangle DEF triangles are similar unequal ratios vertex whole numbers
Σελίδα 99 - IF two triangles have one angle of the one equal to one angle of the other, and the sides about the equal angles proportionals : the triangles shall be equiangular, and shall have those angles equal which are opposite to the homologous sides.
Σελίδα xviii - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 102 - If two similar parallelograms have a common angle, and be similarly situated ; they are about the same diameter.
Σελίδα 99 - Prove that similar triangles are to one another in the duplicate ratio of their homologous sides.
Σελίδα xvi - If the vertical angle of a triangle be bisected by a straight line which also cuts the base, the segments of the base shall have the same ratio which the other sides of the triangle have to one another...
Σελίδα 80 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means.
Σελίδα 99 - ABC, DEF have one angle in the one equal to one angle in the other, viz. the angle BAC to the angle EDF, and the sides about...
Σελίδα 73 - P moves in a plane so that the ratio of its distances from two fixed points A, B in that plane is always the same.
Σελίδα 35 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth: or, if the multiple of the first be equal to that of the second, the multiple of the third is also equal to that of the fourth : or, if...