Elements of Geometry, Geometrical Analysis, and Plane Trigonometry: With an Appendix, Notes and Illustrations |
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Page 30
... . THEOR . The opposite sides of a rhomboid are parallel . If the opposite sides AB , DC , and AD , BC of the qua- drilateral figure ABCD be equal , they are also parallel . For join AC . And because AB is equal to 30 ELEMENTS OF GEOMETRY .
... . THEOR . The opposite sides of a rhomboid are parallel . If the opposite sides AB , DC , and AD , BC of the qua- drilateral figure ABCD be equal , they are also parallel . For join AC . And because AB is equal to 30 ELEMENTS OF GEOMETRY .
Page 31
... ABCD have the sides AB , BC parallel to CD , AD ; these are respectively equal , and so are the opposite angles at A and C , and at B and D. For join AC . Because AB is parallel to CD , the alter- nate angles BAC and ACD are ( I. 25 ...
... ABCD have the sides AB , BC parallel to CD , AD ; these are respectively equal , and so are the opposite angles at A and C , and at B and D. For join AC . Because AB is parallel to CD , the alter- nate angles BAC and ACD are ( I. 25 ...
Page 32
... ABCD intersect each other in E ; the part AE is equal to CE , and DE to BE . For because a rhomboid is also a parallelogram ( I. 28 ) , the alternate angles BAC and ACD are equal ( 1. 25. ) , and likewise ABD and BDC . The tri- angles ...
... ABCD intersect each other in E ; the part AE is equal to CE , and DE to BE . For because a rhomboid is also a parallelogram ( I. 28 ) , the alternate angles BAC and ACD are equal ( 1. 25. ) , and likewise ABD and BDC . The tri- angles ...
Page 36
... ABCD , let the angle at B be equal to the opposite one at D , and the angle at A equal to that at C ; the sides AB , BC are equal and parallel to DC and DA . 1 For all the angles of the figure being equal to 36 ELEMENTS OF GEOMETRY .
... ABCD , let the angle at B be equal to the opposite one at D , and the angle at A equal to that at C ; the sides AB , BC are equal and parallel to DC and DA . 1 For all the angles of the figure being equal to 36 ELEMENTS OF GEOMETRY .
Page 38
... ABCD is the square required . B For , by this construction , the figure has all its sides equal , and one of its angles ABC a right angle ; which comprehends the whole of the definition of a square . PROP . XL . PROB . To divide a given ...
... ABCD is the square required . B For , by this construction , the figure has all its sides equal , and one of its angles ABC a right angle ; which comprehends the whole of the definition of a square . PROP . XL . PROB . To divide a given ...
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Common terms and phrases
ABCD ANALYSIS angle ABC angle ACB angle BAC bisect centre chord circumference COMPOSITION conse consequently the angle decagon describe a circle diameter distance diverging lines drawn equal to BC exterior angle fall the perpendicular given angle given circle given in position given point given ratio given space given straight line greater hence hypotenuse inflected inscribed intercepted intersection isosceles triangle join let fall mean proportional parallel perpendicular point G polygon porism PROB PROP quently radius rectangle rectangle contained regular polygon rhomboid right angle right-angled triangle Scholium segments semicircle semiperimeter sequently side AC similar sine square of AB square of AC tangent THEOR triangle ABC twice the square vertex vertical angle whence wherefore
Popular passages
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 147 - The first and last terms of a proportion are called the extremes, and the two middle terms are called the means.
Page 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
Page 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...
Page 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.
Page 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.
Page 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.
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 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.
Page 60 - 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.