Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Seite 17
... whence ( I. 2. ) the angle CDE or CDG is equal to FDE or FDG . And because , in the triangles DCG and DFG , the side DC is equal to DF , DG common , and the contained angles CDG and FDG are proved to be equal ; these subordinate ...
... whence ( I. 2. ) the angle CDE or CDG is equal to FDE or FDG . And because , in the triangles DCG and DFG , the side DC is equal to DF , DG common , and the contained angles CDG and FDG are proved to be equal ; these subordinate ...
Seite 26
... Whence the angle AGC , being greater than BGC or BCG , which a- gain is greater than ACG , must be still greater than ACG ; and therefore the opposite side AC is ( I. 13. ) greater than AG or DF . PROP . XIX . THEOR . If two sides of 26 ...
... Whence the angle AGC , being greater than BGC or BCG , which a- gain is greater than ACG , must be still greater than ACG ; and therefore the opposite side AC is ( I. 13. ) greater than AG or DF . PROP . XIX . THEOR . If two sides of 26 ...
Seite 29
With an Appendix, and Copious Notes and Illustrations Sir John Leslie. Whence the triangles ABC , DEF are entirely ... Whence , in each of these three cases , the triangle ABC admits of a perfect adaptation with DEF . PROP . XXII ...
With an Appendix, and Copious Notes and Illustrations Sir John Leslie. Whence the triangles ABC , DEF are entirely ... Whence , in each of these three cases , the triangle ABC admits of a perfect adaptation with DEF . PROP . XXII ...
Seite 34
... Whence the side BC is equal to AD , B and the angle ACB equal to CAD ; but these angles being alternate , BC must also be parallel to AD ( I. 22. cor . ) PROP . XXVIII . THEOR . Lines parallel to the 34 ELEMENTS OF GEOMETRY .
... Whence the side BC is equal to AD , B and the angle ACB equal to CAD ; but these angles being alternate , BC must also be parallel to AD ( I. 22. cor . ) PROP . XXVIII . THEOR . Lines parallel to the 34 ELEMENTS OF GEOMETRY .
Seite 44
... Whence the tri- angles ABC and ADC , which are the halves of these rhom- boids ( I. 26. cor . ) , are likewise equivalent . Cor . Hence rhomboids on the same base and between the same parallels , are equivalent . PROP . II . THEOR ...
... Whence the tri- angles ABC and ADC , which are the halves of these rhom- boids ( I. 26. cor . ) , are likewise equivalent . Cor . Hence rhomboids on the same base and between the same parallels , are equivalent . PROP . II . THEOR ...
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Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ... University Professor Emeritus John Leslie, Sir Keine Leseprobe verfügbar - 2016 |
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ABCD adjacent angle altitude angle ABC angle ADB angle BAC base AC bisect centre chord circle circumference consequently construction contained angle cosine decagon denote describe diameter difference distance diverging lines divided draw equal to BC equilateral triangle equivalent to twice evidently exterior angle given greater half Hence hypotenuse inscribed isosceles triangle join let fall likewise measure parallel perpendicular point G polygon PROB PROP Proposition quadrilateral figure quantities radius ratio rectangle rectangle contained rectilineal figure rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter side AC sides AB sine square of AC squares of AB straight line tangent THEOR tion triangle ABC twice the rectangle twice the square vertex vertical angle whence Wherefore
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Seite 30 - ... 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.
Seite 333 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...
Seite 294 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Seite 10 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Seite 137 - 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.
Seite 84 - 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 part of the circumference.
Seite 292 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
Seite 93 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
Seite 38 - 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.
Seite 58 - The rectangle contained by the sum and difference of two straight lines is equivalent to the difference of the squares of these lines.