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
... G , H two sides of the - triangle which it is required to construct . From the centre A , with the distance G , describe a cir- cle ; and , from the centre B , with the distance H , describe another circle , meeting the former in the point ...
... G , H two sides of the - triangle which it is required to construct . From the centre A , with the distance G , describe a cir- cle ; and , from the centre B , with the distance H , describe another circle , meeting the former in the point ...
Seite 15
... point D in the given straight line DE , to form an angle equal to the given angle BAC . In the sides AB and AC of the given angle , assume the points G and H , join GH , from DE cut off DI equal to AG , and on DI consti- tute ( I. 1 ...
... point D in the given straight line DE , to form an angle equal to the given angle BAC . In the sides AB and AC of the given angle , assume the points G and H , join GH , from DE cut off DI equal to AG , and on DI consti- tute ( I. 1 ...
Seite 17
... point above it . 4 From the point C , to let fall a perpendicular upon the given straight line AB . 2 In AB take ... G : CG is perpendicular to AB . For the straight lines DC , DF and EC , EF being joined , the trian- gles DCE and DFE ...
... point above it . 4 From the point C , to let fall a perpendicular upon the given straight line AB . 2 In AB take ... G : CG is perpendicular to AB . For the straight lines DC , DF and EC , EF being joined , the trian- gles DCE and DFE ...
Seite 26
... point G lies beyond H. Next , suppose the side BC or EF to be greater than AB or DE . Where- fore ( I. 12. ) the angle BAC is greater than BCA ; but ( I. 8. ) the exterior angle BHC of the triangle ABH B D H G F is greater than BAH or ...
... point G lies beyond H. Next , suppose the side BC or EF to be greater than AB or DE . Where- fore ( I. 12. ) the angle BAC is greater than BCA ; but ( I. 8. ) the exterior angle BHC of the triangle ABH B D H G F is greater than BAH or ...
Seite 30
... point G , it makes an angle EFH greater than EGA ; G H I K and when it meets AB below that B / point , it makes an angle EFL , E which is less than the same angle . But in passing through all the degrees from greater to less , a varying ...
... point G , it makes an angle EFH greater than EGA ; G H I K and when it meets AB below that B / point , it makes an angle EFL , E which is less than the same angle . But in passing through all the degrees from greater to less , a varying ...
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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.