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### Inhalt

 Lines and Planes 1 Angles 9 Circles 25 Triangles 41 Parallels and Quadrilaterals 51 Areas 76 Proportion 96 Numerical Proportion Definition of Term Extreme Mean Pro 116
 Tangents 140 Combinations of Circles 161 Similar Figures 186 Polygons 199 Equality and Similarity of Polygons 232 Miscellaneous Problems 261 RECAPITULATION OF PRINCIPAL THEOREMS AND PRO 267 INDEX 274

### Beliebte Passagen

Seite 33 - Any two sides of a triangle are together greater than the third side.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 153 - Describe a circle which shall pass through two given points, and have its centre in a given line.
Seite 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.
Seite 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.
Seite 264 - To prove that the exterior angle of a triangle is equal to the sum of the two interior opposite angles (see fig.
Seite 11 - I., 5), (3) that, if two straight lines cut one another, the vertically opposite angles are equal (Eucl.