## Elements of Geometry, Geometrical Analysis, and Plane Trigonometry ... |

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alternate ANALYSIS base bisect Book centre chord circle circumference common COMPOSITION consequently construction contained corresponding denote diameter difference distance diverging lines divided double draw drawn equal equivalent evidently expression extended extreme figure follows fore four given circle given in position given point given ratio given space greater half hence inflected inscribed intercepted intersection join let fall likewise mean measure meet opposite parallel perpendicular point F polygon portion PROB problem produce PROP proportional proposition quantities radius ratio reason rectangle regular remaining right angles segments semicircle sides similar sine square straight line tangent THEOR third tion triangle triangle ABC twice vertical angle whence wherefore whole

### Popular passages

Page 460 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...

Page 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.

Page 145 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.

Page 34 - 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.

Page 153 - 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.

Page 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...

Page 411 - 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.

Page 58 - Prove, geometrically, that the rectangle of the sum and the difference of two straight lines is equivalent to the difference of the squares of those lines.

Page 64 - IF a straight line be bisected, and produced to any point: the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...

Page 157 - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.