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

### From inside the book

Results 1-5 of 23

Page xv

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**given**lines , 263. If the sides of an angle are divided proportionately , the straight lines joining the division ...**number**of equal parts , 278. Proportions formed by letting fall**a**perpendicular from the ver- tex of**a**right - angled ... Page 17

... 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

... 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 ... Page 18

... number of points of inter- section , which a

... number of points of inter- section , which a

**given 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 ... Page 20

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**number**of points , we must multiply the**numbers**of the two sets together and add 1 to the product . Example . Divide ...**given**, ( 22. ) The**number**20 , for example , being divided 2 x 1 Into 18 and 2 , gives ( 20 RECKONING AND ... Page 23

... number in the 3 sets to be 4 , 4 , 4 6 , 6 , 6 2 , 3 , 4 2,3 , 3 , 4 , 5 66 " L ፡፡ 3 , 3 , 3 we have ( 3 × 3 ) + ...

... number in the 3 sets to be 4 , 4 , 4 6 , 6 , 6 2 , 3 , 4 2,3 , 3 , 4 , 5 66 " L ፡፡ 3 , 3 , 3 we have ( 3 × 3 ) + ...

**given number**of points , of which only two lie in the same direction . 1. Between 2 points , only 1 straight ...### 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.