Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Seite 12
... reason , BC is equal to H. Consequently the triangle ACB answers the conditions of the problem . The limiting circles , after mutually intersect- ing , must obviously diverge from each other , till , crossing the extension of the base ...
... reason , BC is equal to H. Consequently the triangle ACB answers the conditions of the problem . The limiting circles , after mutually intersect- ing , must obviously diverge from each other , till , crossing the extension of the base ...
Seite 13
... reason , B must be found in the circumference of a circle de- scribed from E with the distance D EA EF : The vertex of the triangle ACB must , therefore , ap- pear in a point which is common to both those circles , or , by the first ...
... reason , B must be found in the circumference of a circle de- scribed from E with the distance D EA EF : The vertex of the triangle ACB must , therefore , ap- pear in a point which is common to both those circles , or , by the first ...
Seite 24
... reason , DEC is greater than ABE , the opposite in- terior angle of the triangle EAB . Consequently ADC is still greater than ABE or ABC . PROP . XVII . THEOR , If straight lines be drawn from the same point to another straight line ...
... reason , DEC is greater than ABE , the opposite in- terior angle of the triangle EAB . Consequently ADC is still greater than ABE or ABC . PROP . XVII . THEOR , If straight lines be drawn from the same point to another straight line ...
Seite 25
... reason , the angle CED of the triangle CDE is acute , and consequently its adjacent angle CEG is obtuse . Where- fore CEG , being greater than a right angle , is still greater than CGE , and the opposite side CG must be greater ( I. 13 ...
... reason , the angle CED of the triangle CDE is acute , and consequently its adjacent angle CEG is obtuse . Where- fore CEG , being greater than a right angle , is still greater than CGE , and the opposite side CG must be greater ( I. 13 ...
Seite 28
... reason , the an- gles BCA and EFD being equal , the side CB must lie a- long FE . Wherefore the point B , which is common to both the lines AB and CB , will be found likewise in both DE and FE ; that is , it must fall upon the ...
... reason , the an- gles BCA and EFD being equal , the side CB must lie a- long FE . Wherefore the point B , which is common to both the lines AB and CB , will be found likewise in both DE and FE ; that is , it must fall upon the ...
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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.