Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 páginas |
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Página 18
... THEOR . The exterior angle of a triangle is greater than either of its interior opposite angles . The exterior angle BCF , formed by producing a side AC of the triangle ABC , is greater than either of the op- posite and interior angles ...
... THEOR . The exterior angle of a triangle is greater than either of its interior opposite angles . The exterior angle BCF , formed by producing a side AC of the triangle ABC , is greater than either of the op- posite and interior angles ...
Página 19
... THEOR . Any two angles of a triangle are together less than two right angles . ۱ The two angles BAC and BCA of the triangle ABC are together less than two right angles . B For produce the common side AC . And , by the last proposition ...
... THEOR . Any two angles of a triangle are together less than two right angles . ۱ The two angles BAC and BCA of the triangle ABC are together less than two right angles . B For produce the common side AC . And , by the last proposition ...
Página 20
... THEOR . The angles at the base of an isosceles triangle are equal . The angles BAC and BCA at the base of the isosceles triangle ABC are equal . For draw ( I. 5. ) BD bisecting the vertical angle ABC . Because , by hypothesis , AB is ...
... THEOR . The angles at the base of an isosceles triangle are equal . The angles BAC and BCA at the base of the isosceles triangle ABC are equal . For draw ( I. 5. ) BD bisecting the vertical angle ABC . Because , by hypothesis , AB is ...
Página 21
... THEOR . In any triangle , that angle is the greater which lies opposite to a greater side . If a side BC of the triangle ABC be greater than BA ; the opposite angle BAC is greater than BCA . For make BD equal to BA , and join AD . The ...
... THEOR . In any triangle , that angle is the greater which lies opposite to a greater side . If a side BC of the triangle ABC be greater than BA ; the opposite angle BAC is greater than BCA . For make BD equal to BA , and join AD . The ...
Página 23
... THEOR . The difference between two sides of a triangle is less than the third side . Let the side AC be greater than AB , and from it cut off a part AE equal to AB ; the remainder EC is less than the third side BC . For the two sides AB ...
... THEOR . The difference between two sides of a triangle is less than the third side . Let the side AC be greater than AB , and from it cut off a part AE equal to AB ; the remainder EC is less than the third side BC . For the two sides AB ...
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Otras ediciones - Ver todas
Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ... University Professor Emeritus John Leslie, Sir Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD adjacent angle altitude angle ABC angle ADB angle BAC angle BCD 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 Geometry greater half Hence hypotenuse inscribed intercepted 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 sinAC sinB sine square of AB square of AC tangent THEOR tion triangle ABC twice the rectangle twice the square vertex vertical angle whence Wherefore
Pasajes populares
Página 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.
Página 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...
Página 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...
Página 10 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 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.
Página 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.
Página 292 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
Página 93 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
Página 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.
Página 58 - The rectangle contained by the sum and difference of two straight lines is equivalent to the difference of the squares of these lines.