Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Seite 33
... ABCD be equal , they are also parallel . For draw the diagonal AC . And because AB is equal to DC , BC to AD , and AC is com- mon ; the two triangles ABC and ADC are ( I. 2. ) equal . Conse- quently the angle ACD is equal D C to CAB ...
... ABCD be equal , they are also parallel . For draw the diagonal AC . And because AB is equal to DC , BC to AD , and AC is com- mon ; the two triangles ABC and ADC are ( I. 2. ) equal . Conse- quently the angle ACD is equal D C to CAB ...
Seite 39
... ABCD , let the angle at B be equal to the opposite one at D , and the angle at A equal to that at C ; the sides AB and BC are equal and parallel to DC and DA . For all the angles of the figure being equal to four right angles ( I. 31 ...
... ABCD , let the angle at B be equal to the opposite one at D , and the angle at A equal to that at C ; the sides AB and BC are equal and parallel to DC and DA . For all the angles of the figure being equal to four right angles ( I. 31 ...
Seite 41
... ABCD is the square required . D B For , by this construction , the figure has all its sides e- qual , and one of its angles ABC a right angle ; which com- prehends the whole of the definition of a square . PROP . XXXVI . PROB . To ...
... ABCD is the square required . D B For , by this construction , the figure has all its sides e- qual , and one of its angles ABC a right angle ; which com- prehends the whole of the definition of a square . PROP . XXXVI . PROB . To ...
Seite 51
... ABCD is equivalent to the rectangle con- tained by its altitude and half the sum of the parallel sides BC and AD . For draw CE parallel to AB ( I. 23. ) , bisect ED ( I. 7. ) in F , and draw FG parallel to AB , meeting the production of ...
... ABCD is equivalent to the rectangle con- tained by its altitude and half the sum of the parallel sides BC and AD . For draw CE parallel to AB ( I. 23. ) , bisect ED ( I. 7. ) in F , and draw FG parallel to AB , meeting the production of ...
Seite 69
... ABCD be a rhomboid : The squares of all the sides AB , BC , CD , and AD , are together equivalent to the squares of the diagonals AC , BD . A B E D For the angles BCE and CBE are equal to the alternate angles DAE and ADE , and the ...
... ABCD be a rhomboid : The squares of all the sides AB , BC , CD , and AD , are together equivalent to the squares of the diagonals AC , BD . A B E D For the angles BCE and CBE are equal to the alternate angles DAE and ADE , and the ...
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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 |
Häufige Begriffe und Wortgruppen
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.