Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 páginas |
Dentro del libro
Resultados 1-5 de 71
Página 40
... half of CDB . But the triangle BDC being isosceles , the angle CBD is equal to BCD ; consequently the angles DBF and DBC are the halves of the vertical and base angles of BDC , and therefore ( I. 30. ) the whole angle CBF is the half of ...
... half of CDB . But the triangle BDC being isosceles , the angle CBD is equal to BCD ; consequently the angles DBF and DBC are the halves of the vertical and base angles of BDC , and therefore ( I. 30. ) the whole angle CBF is the half of ...
Página 48
... half the base . The triangle ABC is equivalent to the rhomboid DEFC , which stands on half the base DC , but has the same alti- tude . B E T For join BD and EC . The triangles ABD and DBC having the same vertex and equal bases , are ...
... half the base . The triangle ABC is equivalent to the rhomboid DEFC , which stands on half the base DC , but has the same alti- tude . B E T For join BD and EC . The triangles ABD and DBC having the same vertex and equal bases , are ...
Página 51
... half the sum of BC and AD . Wherefore the rectangle contained by the altitude of the trapezoid and half the sum of its pa- rallel sides , is equivalent to the rhomboid BF ( II . 1. cor . ) ; but the rhomboid EG is equivalent to the ...
... half the sum of BC and AD . Wherefore the rectangle contained by the altitude of the trapezoid and half the sum of its pa- rallel sides , is equivalent to the rhomboid BF ( II . 1. cor . ) ; but the rhomboid EG is equivalent to the ...
Página 59
... half line AC , is equivalent to the square of CD , which is made up of the half line and the produced part . For AD is the sum of AC , CD , and DB is their difference ; whence the rectangle AD , DB is equivalent to B D the excess of the ...
... half line AC , is equivalent to the square of CD , which is made up of the half line and the produced part . For AD is the sum of AC , CD , and DB is their difference ; whence the rectangle AD , DB is equivalent to B D the excess of the ...
Página 60
... half their sum and of half their difference . Let AB , BC be two continuous straight lines , D the middle point of AC , and consequently AD half the sum of these lines and DB half their difference ; the squares of AB and BC are together ...
... half their sum and of half their difference . Let AB , BC be two continuous straight lines , D the middle point of AC , and consequently AD half the sum of these lines and DB half their difference ; the squares of AB and BC are together ...
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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 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
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.