## 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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**line**into any**number**of equal parts , 278. Proportions formed by letting fall a perpendicular from the ver- tex of a right - angled triangle , . 147 · 147 148 279. To find a mean proportional between two given**lines**, 280. To transform ... Page 12

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**lines**where the several parts of the bodies unite , so that the paste- board ...**line**, plane , and solid angles , all the faces , and all the sides ...**number**of seats or faces in the solid . 1. The tetraedron , which is bounded ... Page 17

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**numbers**from one up to , and including , that**number**which denotes the**number**of the given points . 22. What is the greatest**number**of points at which any given**number**of straight**lines**may intersect one another ? Answer . 2 straight**lines**... Page 18

... number of straight lines may make : add together the natural series of numbers from 1 up to , but without including , that number which makes the

... number of straight lines may make : add together the natural series of numbers from 1 up to , but without including , that number which makes the

**number of lines**. 1 line gives 0 points . 2 lines give 3 66 66 1 + 2 20 66 " 1 66 = 3 ... Page 19

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**lines**are divided into 2 sets , one of which has 4**lines**and the other 2**lines**; the 4 are paral- lel one to the other , and the 2 are parallel to each other . What is the greatest**number**of intersection points ? Answer . Each**line**of ...### 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.