An Elementary Course of Plane Geometry

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Thomas Murray, 1870 - 16 páginas

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Página 33 - Any two sides of a triangle are together greater than the third side.
Página 266 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Página vi - In my own time," says Seneca, "there have been inventions of this sort, transparent windows, tubes for diffusing warmth equally through all parts of a building, short-hand, which has been carried to such a perfection that a writer can keep pace with the most rapid speaker. But the inventing of such things is drudgery for the lowest slaves; philosophy lies deeper. It is not her office to teach men how to use their hands.
Página 59 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Página 146 - If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment.
Página 153 - Describe a circle which shall pass through two given points, and have its centre in a given line.
Página 68 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the transversal is equal to two right angles, (p.
Página 86 - If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the two parts.
Página 264 - To prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles (see fig.
Página 11 - I., 5), (3) that, if two straight lines cut one another, the vertically opposite angles are equal (Eucl.

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