Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Seite 13
... figure may be divided into triangles , which , being separately constructed with the same corresponding sides , must , by their combi- nation , hence form an equal figure . PROP . III . THEOR . Two triangles are equal BOOK I. / 13.
... figure may be divided into triangles , which , being separately constructed with the same corresponding sides , must , by their combi- nation , hence form an equal figure . PROP . III . THEOR . Two triangles are equal BOOK I. / 13.
Seite 27
... than DF . PROP . XX . THEOR . Two triangles are equal , which have two angles and a corresponding side in the one respectively equal to those in the other . Let the triangles ABC and DEF have the angle BAC BOOK I. 27.
... than DF . PROP . XX . THEOR . Two triangles are equal , which have two angles and a corresponding side in the one respectively equal to those in the other . Let the triangles ABC and DEF have the angle BAC BOOK I. 27.
Seite 28
... corresponding vertex E. The two triangles ABC and DEF , thus mu- tually adapting , are hence entirely equal . CD Next , let the equal sides be AB and DE , which are op- posite to the equal angles BCA and EFD . The triangle ABC being ...
... corresponding vertex E. The two triangles ABC and DEF , thus mu- tually adapting , are hence entirely equal . CD Next , let the equal sides be AB and DE , which are op- posite to the equal angles BCA and EFD . The triangle ABC being ...
Seite 29
... forms it , can , for the same rea- son , have only one corresponding position . - Whence , in each of these three cases , the triangle ABC admits of a perfect adaptation with DEF . PROP . XXII . THEOR . If a straight line BOOK I. 29.
... forms it , can , for the same rea- son , have only one corresponding position . - Whence , in each of these three cases , the triangle ABC admits of a perfect adaptation with DEF . PROP . XXII . THEOR . If a straight line BOOK I. 29.
Seite 37
... corresponding angle in the other . Schol . On the second corollary depends the construction of that invaluable reflecting angular instrument , called Hadley's quadrant or sextant . PROP . XXXI . THEOR . The interior angles of any ...
... corresponding angle in the other . Schol . On the second corollary depends the construction of that invaluable reflecting angular instrument , called Hadley's quadrant or sextant . PROP . XXXI . THEOR . The interior angles of any ...
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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.