Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and Illustrations |
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Page 5
... common to them both , being placed in the middle . Thus , the angle con- tained by the straight lines AB and BC , or the opening formed by turning BA about the point B into the position BC , is named ABC or CBA . A- 4. A right angle is ...
... common to them both , being placed in the middle . Thus , the angle con- tained by the straight lines AB and BC , or the opening formed by turning BA about the point B into the position BC , is named ABC or CBA . A- 4. A right angle is ...
Page 7
... common angle ABD , there remains CBA equal to DBE . 11. Two straight lines are said to be inclined to each other , if they meet when produced ; and the an- gle so formed is called their inclination . 12. Straight lines which have no in ...
... common angle ABD , there remains CBA equal to DBE . 11. Two straight lines are said to be inclined to each other , if they meet when produced ; and the an- gle so formed is called their inclination . 12. Straight lines which have no in ...
Page 13
... common to both those circles , or , by the first proposition , in F the vertex of the triangle DFE . Consequently these two triangles , being rectilineal , must entirely coincide . The angle CAB is equal to EDF , ACB to DEF , and CBA to ...
... common to both those circles , or , by the first proposition , in F the vertex of the triangle DFE . Consequently these two triangles , being rectilineal , must entirely coincide . The angle CAB is equal to EDF , ACB to DEF , and CBA to ...
Page 16
... common to both , are ( I. 2. ) equal , and consequently the angle DBF is equal to EBF . E Cor . Hence the mode of drawing a perpendicular from a given point B in the straight line AC ; for the angle ABC , which the opposite seg- F ments ...
... common to both , are ( I. 2. ) equal , and consequently the angle DBF is equal to EBF . E Cor . Hence the mode of drawing a perpendicular from a given point B in the straight line AC ; for the angle ABC , which the opposite seg- F ments ...
Page 17
... common to them both ; 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 ...
... common to them both ; 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 ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 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...
Page 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...
Page 10 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 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.
Page 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.
Page 292 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
Page 93 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
Page 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.
Page 58 - The rectangle contained by the sum and difference of two straight lines is equivalent to the difference of the squares of these lines.