Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Seite 56
... The square described on the sum of two straight lines , is equivalent to the squares of those lines , together with twice their rectangle . If AB and BC be two straight lines placed continuous ; the square described on their sum AC , is ...
... The square described on the sum of two straight lines , is equivalent to the squares of those lines , together with twice their rectangle . If AB and BC be two straight lines placed continuous ; the square described on their sum AC , is ...
Seite 57
... the square of AC is divid- ed , are all rhomboidal and rectangu- lar . And because AB is equal to AF , and the ... twice the rectangle contained by these lines . PROP . XVI . THEOR . The square described on the difference of two straight ...
... the square of AC is divid- ed , are all rhomboidal and rectangu- lar . And because AB is equal to AF , and the ... twice the rectangle contained by these lines . PROP . XVI . THEOR . The square described on the difference of two straight ...
Seite 58
... twice the rectangle under AB and BC , —and there remains ADEC , or the square of the difference AC of the two lines AB and BC . PROP . XVII . THEOR . The rectangle contained by the sum and diffe- rence of two straight lines , is ...
... twice the rectangle under AB and BC , —and there remains ADEC , or the square of the difference AC of the two lines AB and BC . PROP . XVII . THEOR . The rectangle contained by the sum and diffe- rence of two straight lines , is ...
Seite 60
... squares of AB and BC are together equivalent to twice the square of AD , with twice the square of DB . For erect ( I. 5. cor . ) the perpendicular DE equal to AD or DC , join AE and EC , through B and F draw ( I. 23. ) BF and FG ...
... squares of AB and BC are together equivalent to twice the square of AD , with twice the square of DB . For erect ( I. 5. cor . ) the perpendicular DE equal to AD or DC , join AE and EC , through B and F draw ( I. 23. ) BF and FG ...
Seite 61
... twice the square of GF or of DB ; and the square of AE , in the right angled tri- angle ADE , is equivalent to the squares of AD and DE , or twice the square of AD . But since ABF is a right an- gle , the square of AF is equivalent to ...
... twice the square of GF or of DB ; and the square of AE , in the right angled tri- angle ADE , is equivalent to the squares of AD and DE , or twice the square of AD . But since ABF is a right an- gle , the square of AF is equivalent to ...
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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.