## An Introduction to Geometry and the Science of Form: Prepared from the Most Approved Prussian Text-books |

### From inside the book

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Page xii

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**vertices**, 157. Value of the exterior angles of a polygon , 90 . 91 91 • 91 220 92 92 94 95 95 96 . 96 96 97 158. Table of the size of angles in a regular figure , and surface , 159. Mensuration of a rectilineal figure . Superficial ... Page 14

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**vertices**of any two angles of a polygon , which are not already connected by one of the bounding lines . 18. Tell me all that you remark in this figure . ( Fig . 13. ) Figures . Rectilineal . The same as in fig . 12 . Curvilineal . 1 ... Page 26

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**vertices**; each is connected with 2 others by the bounding lines ; therefore from each vertex only 2 diagonals can be drawn ; from the 5**vertices**2 × 5 = 10 ; but this is double the real num- 2X5 ber , which is = 5 . 2 4. If we extend ... Page 42

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**vertices**of 2 other angles ; there remain then just as many**vertices**with which each vertex is not connected , as the figure has sides less 3 . Consequently there may be as many diagonals not in- tersecting one another , as the ... Page 61

... to the circle at the division points , and produce such tangents in both directions until they intersect one another , and we have a scalene triangle about a circle . Remark . The

... to the circle at the division points , and produce such tangents in both directions until they intersect one another , and we have a scalene triangle about a circle . Remark . The

**vertices**of all the angles of each FIGURES . 61.### Other editions - View all

### Common terms and phrases

adjacent angles angle BAC angles are equal Bisect centre chord circumference coincide concave angles consequently angle construct a square convex angle convex surface cube curved line cylinder decagonal describe a circle diagonals diameter divided division points draw a line Draw a straight equal altitude equal angles equal bases equivalent erect a perpendicular exterior angles feet found by multiplying given number given square greatest number hexagon homologous sides hypothenuse inches inscribed circle isosceles triangle length let fall line drawn line passes magnitude measured Multiply the number number of lines number of points number of straight opposite parallelogram parallelopiped passes 2 points pendicular pentagon proportion protractor quadrilateral radii radius equal ratio regular polygon right angle semi-circumference set intersecting side AC similar similar triangles solidity sphere straight line suppose tangents triangle ABC triangular prism unequal vertex vertices

### Popular passages

Page 130 - The first and fourth terms of a proportion are called the extremes, and the second and third terms, the means. Thus, in the foregoing proportion, 8 and 3 are the extremes and 4 and 6 are the means.

Page 154 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.