Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Seite 13
... side AB equal to DF , AC to DE , and BC to FE : These triangles are equal . For conceive the triangle ACB to be applied to DEF : The point A being laid on D , and the side AC on DE , their other extremities C and E must coincide , since ...
... side AB equal to DF , AC to DE , and BC to FE : These triangles are equal . For conceive the triangle ACB to be applied to DEF : The point A being laid on D , and the side AC on DE , their other extremities C and E must coincide , since ...
Seite 14
... side AB is equal to DE , the side BC to EF , and the angle ABC contained by the former equal to DEF which is ... AC and DF will also coincide . Wherefore , the one triangle being thus per- fectly adapted to the other , a general equality must ...
... side AB is equal to DE , the side BC to EF , and the angle ABC contained by the former equal to DEF which is ... AC and DF will also coincide . Wherefore , the one triangle being thus per- fectly adapted to the other , a general equality must ...
Seite 16
... sides AB and BC of the given angle be supposed equal , only one circle would be ... side even make repeated revolutions . PROP . V. PROB . To bisect a given ... AC ; for the angle ABC , which the opposite seg- F ments BA and BC make with ...
... sides AB and BC of the given angle be supposed equal , only one circle would be ... side even make repeated revolutions . PROP . V. PROB . To bisect a given ... AC ; for the angle ABC , which the opposite seg- F ments BA and BC make with ...
Seite 17
... AC . Schol . In the general construction , the isosceles triangle DFE may stand either below or above the base DE ... side DC equal to DF , EC to EF , and -B E DE common to them both ; whence ( I. 2. ) the angle CDE or CDG is equal to FDE or ...
... AC . Schol . In the general construction , the isosceles triangle DFE may stand either below or above the base DE ... side DC equal to DF , EC to EF , and -B E DE common to them both ; whence ( I. 2. ) the angle CDE or CDG is equal to FDE or ...
Seite 18
... sides AC and AD of the triangle CAD being respectively equal to BC and BD of the triangle CBD , and the side CD common to them both ; these triangles ( I. 2. ) are equal , and the angle ACD or ACE is equal to BCD or BCE . Again , the ...
... sides AC and AD of the triangle CAD being respectively equal to BC and BD of the triangle CBD , and the side CD common to them both ; these triangles ( I. 2. ) are equal , and the angle ACD or ACE is equal to BCD or BCE . Again , 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 |
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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.