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 26
Page xv
... two inaccessible objects , 277. To divide a straight 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 ...
... two inaccessible objects , 277. To divide a straight 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 ...
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 given number of straight lines may intersect one another ? Answer . 2 straight ...
... 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 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 ...
... 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
... number of lines which will give 45 points of intersection is 10 . 24. The intersecting straight lines may be divided into many sets . We will first suppose them to be divided into 2 sets , and will consider several different cases . 1 ...
... number of lines which will give 45 points of intersection is 10 . 24. The intersecting straight lines may be divided into many sets . We will first suppose them to be divided into 2 sets , and will consider several different cases . 1 ...
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 ) + ... straight lines may be drawn between a given number of points , of which only two lie in the same direction . 1 ...
... 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 ) + ... straight lines may be drawn between a given number of points , of which only two lie in the same direction . 1 ...
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.