Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
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Seite 101
... 2. A rectilineal figure circumscribes a circle , when each of its sides is a tan- gent . 3. A circle is inscribed in a rectilineal figure , when it touches all the sides . 4. A circle is described about a rectili- neal figure ELEMENTS ...
... 2. A rectilineal figure circumscribes a circle , when each of its sides is a tan- gent . 3. A circle is inscribed in a rectilineal figure , when it touches all the sides . 4. A circle is described about a rectili- neal figure ELEMENTS ...
Seite 111
... inscribe a circle . Let ABC be a triangle , it which it is required to in- scribe a circle . Draw AD and CD ( I. 5 ... inscribe a triangle equian- gular to a given triangle . Let GDH be a circle , in which it is required to inscribe a ...
... inscribe a circle . Let ABC be a triangle , it which it is required to in- scribe a circle . Draw AD and CD ( I. 5 ... inscribe a triangle equian- gular to a given triangle . Let GDH be a circle , in which it is required to inscribe a ...
Seite 113
... inscribed in a circle to any point in the opposite circumference , is equal to the two chords inflected from the same point to the extremities of the base . Let ABC be an equilateral triangle inscribed in a cir- cle , and BD , AD , and ...
... inscribed in a circle to any point in the opposite circumference , is equal to the two chords inflected from the same point to the extremities of the base . Let ABC be an equilateral triangle inscribed in a cir- cle , and BD , AD , and ...
Seite 114
... inscribe a circle . Let ABCD be a square , about which it is required to circumscribe a circle . Draw the diagonals AC , DB intersecting each other in O , and , from that point with the distance AO , describe the circle ABCD : This ...
... inscribe a circle . Let ABCD be a square , about which it is required to circumscribe a circle . Draw the diagonals AC , DB intersecting each other in O , and , from that point with the distance AO , describe the circle ABCD : This ...
Seite 115
... inscribe a circle in the square ABCD . B R S P B From O the intersection of the diagonals and with its distance from ... inscribed within a given square . For let tangents be applied at the points I , K , L , and M , where the diagonals ...
... inscribe a circle in the square ABCD . B R S P B From O the intersection of the diagonals and with its distance from ... inscribed within a given square . For let tangents be applied at the points I , K , L , and M , where the diagonals ...
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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.