Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Seite 6
... a right angle . 7. An obtuse angle is greater than a right angle . 8. One side of an angle forms with the other produced a supplemental or exterior angle . 9. A verticat angle is formed by the production of 6 ELEMENTS OF GEOMETRY .
... a right angle . 7. An obtuse angle is greater than a right angle . 8. One side of an angle forms with the other produced a supplemental or exterior angle . 9. A verticat angle is formed by the production of 6 ELEMENTS OF GEOMETRY .
Seite 9
... greater than two right angles , it makes a sinuosity , and is termed re - entrant . Thus the angle ABC is re - entrant , and the rest of the angles of the polygon ABCDEF are salient at A , C , D , E and F. D I B F 32. A rectilineal ...
... greater than two right angles , it makes a sinuosity , and is termed re - entrant . Thus the angle ABC is re - entrant , and the rest of the angles of the polygon ABCDEF are salient at A , C , D , E and F. D I B F 32. A rectilineal ...
Seite 18
... greater than either of its interior opposite angles . B 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 CAB and CBA . For bisect the side BC in ...
... greater than either of its interior opposite angles . B 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 CAB and CBA . For bisect the side BC in ...
Seite 19
... greater than DCE ; it is con- sequently greater than DBA or CBA . In like manner , it may be shown , that if BC be produ- ced , the exterior angle ACG is greater than CAB . But ACG is equal to the vertical angle BCF , and hence BCF must ...
... greater than DCE ; it is con- sequently greater than DBA or CBA . In like manner , it may be shown , that if BC be produ- ced , the exterior angle ACG is greater than CAB . But ACG is equal to the vertical angle BCF , and hence BCF must ...
Seite 21
... 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 . B For make BD equal to BA , and join AD . The angle CAB is evidently greater than DAB ...
... 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 . B For make BD equal to BA , and join AD . The angle CAB is evidently greater than DAB ...
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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.