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alternate ANALYSIS base bisect Book centre chord circle circumference common COMPOSITION consequently construction contained corresponding diameter difference distance diverging lines divided double draw drawn equal equivalent evidently expression extended extreme figure follows fore four fourth given circle given in position given point given ratio given space greater half hence inflected inscribed intercepted intersection join let fall likewise measure meet opposite parallel perpendicular point F polygon portion PROB problem produce PROP proposition quantities radius ratio reason rectangle regular remaining right angles segments semicircle sides similar sine square straight line successive tangent THEOR third tion triangle triangle ABC twice vertical angle whence wherefore whole
Pàgina 28 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Pàgina 92 - THE angle at the centre of a circle is double of the angle at the circumference, upon the same base, that is, upon the same
Pàgina 458 - 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...
Pàgina 99 - ... a circle. The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle. The opposite angles of any quadrilateral inscribed in a circle are supplementary; and the converse.
Pàgina 155 - Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth.
Pàgina 408 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Pàgina 16 - PROP. V. THEOR. The angles at the base of an isosceles triangle are equal to one another; and if the equal sides be produced, the angles -upon the other side of the base shall be equal. Let ABC be an isosceles triangle, of which the side AB is equal to AC, and let the straight lines AB, AC, be produced to D and E: the angle ABC shall be equal to the angle ACB, and the angle...
Pàgina 36 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.