Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 páginas |
Dentro del libro
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Página 7
... angle is formed by the production of both its sides . 10. The inverted divergence of the two sides of an an- gle , or the defect of the angle from four right angles , is named the reverse angle . The angle DBE is vertical to ABC , ABD ...
... angle is formed by the production of both its sides . 10. The inverted divergence of the two sides of an an- gle , or the defect of the angle from four right angles , is named the reverse angle . The angle DBE is vertical to ABC , ABD ...
Página 19
... vertical angle BDA equal to CDE ; these triangles are , therefore , equal ( I. 3. ) , and the angle DCE is equal to DBA . But the angle BCF is evidently greater than DCE ; it is con- sequently greater than DBA or CBA . In like manner ...
... vertical angle BDA equal to CDE ; these triangles are , therefore , equal ( I. 3. ) , and the angle DCE is equal to DBA . But the angle BCF is evidently greater than DCE ; it is con- sequently greater than DBA or CBA . In like manner ...
Página 20
... 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 equal to BC ...
... 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 equal to BC ...
Página 27
... angle contained by the former will be likewise greater than what is contained by the lat- ter . Let the triangles ABC and DEF have the sides AB and BC equal to DE and EF , but the base AC greater than DF ; the vertical angle ABC is ...
... angle contained by the former will be likewise greater than what is contained by the lat- ter . Let the triangles ABC and DEF have the sides AB and BC equal to DE and EF , but the base AC greater than DF ; the vertical angle ABC is ...
Página 30
... angle equal to the interior opposite one , and the two interior angles on the same side to- gether equal to two ... vertical angle GFK in the triangle FKG , and to which the A CL angle FGA is exterior ; conse- H quently ( I. 8 ...
... angle equal to the interior opposite one , and the two interior angles on the same side to- gether equal to two ... vertical angle GFK in the triangle FKG , and to which the A CL angle FGA is exterior ; conse- H quently ( I. 8 ...
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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.