Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Seite 10
... diameter of a circle is a straight line drawn through the centre , and terminated both ways by the cir- cumference ... diameters . 36. Figures are said to be equal , when , applied to each other , they wholly coincide ; they are ...
... diameter of a circle is a straight line drawn through the centre , and terminated both ways by the cir- cumference ... diameters . 36. Figures are said to be equal , when , applied to each other , they wholly coincide ; they are ...
Seite 73
... diameter . The circle ADBE is divided into two equal portions , by the diameter AB . D For let the portion ADB be reversed and applied to AEB , the straight line AB and its middle point , or the centre C , re- maining the same . And ...
... diameter . The circle ADBE is divided into two equal portions , by the diameter AB . D For let the portion ADB be reversed and applied to AEB , the straight line AB and its middle point , or the centre C , re- maining the same . And ...
Seite 76
... diameter EF ( I. 7. ) , and bị- secting this again in G. PROP . VI . THEOR . The diameter is the greatest line that can be inflected within a circle . The diameter AB is greater than any chord DE . D E B For join CD and CE . The two ...
... diameter EF ( I. 7. ) , and bị- secting this again in G. PROP . VI . THEOR . The diameter is the greatest line that can be inflected within a circle . The diameter AB is greater than any chord DE . D E B For join CD and CE . The two ...
Seite 77
... diameter , is greater than AE . For the triangles ADC and AEC have the side CD equal to CE , the side CA common to both , but the contained angle DCA greater than ECA ; wherefore ( I. 18. ) the base AD is likewise great- er than the ...
... diameter , is greater than AE . For the triangles ADC and AEC have the side CD equal to CE , the side CA common to both , but the contained angle DCA greater than ECA ; wherefore ( I. 18. ) the base AD is likewise great- er than the ...
Seite 78
... diameter . Let A be a point which is not the centre of the circle , and AD a straight line drawn from it to the circumference . Find the centre C ( III . 5. cor . ) join CA and CD , draw ( I. 4. ) CE making an angle ACE equal to ACD and ...
... diameter . Let A be a point which is not the centre of the circle , and AD a straight line drawn from it to the circumference . Find the centre C ( III . 5. cor . ) join CA and CD , draw ( I. 4. ) CE making an angle ACE equal to ACD and ...
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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.