An Introduction to Geometry and the Science of Form: Prepared from the Most Approved Prussian Text-books |
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Page xv
... points will be parallel , 138 264 . to 269 . } What determines the similarity of triangles , 139 270. To construct ... number of equal parts , 278. Proportions formed by letting fall a perpendicular from the ver- 147 tex of a right ...
... points will be parallel , 138 264 . to 269 . } What determines the similarity of triangles , 139 270. To construct ... number of equal parts , 278. Proportions formed by letting fall a perpendicular from the ver- 147 tex of a right ...
Page 17
... point , the number of the preceding ways has been multiplied by the number which denotes the present number of points . Therefore to find the number of different combinations which can be made with any number of points ; Mul- tiply ...
... point , the number of the preceding ways has been multiplied by the number which denotes the present number of points . Therefore to find the number of different combinations which can be made with any number of points ; Mul- tiply ...
Page 18
... 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 2 ...
... 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 2 ...
Page 19
... number of lines which will give 45 points of intersection is 10 . 24. The intersecting straight lines may be divided ... number of intersection points ? Answer . Each line of one set intersects each line of the other set , thus we ...
... number of lines which will give 45 points of intersection is 10 . 24. The intersecting straight lines may be divided ... number of intersection points ? Answer . Each line of one set intersects each line of the other set , thus we ...
Page 20
... point . In this case each line of the second set intersects each line of the first set , and the lines of the second set give one intersection point besides . To ascertain the whole number of points , we must multiply the numbers of the ...
... point . In this case each line of the second set intersects each line of the first set , and the lines of the second set give one intersection point besides . To ascertain the whole number of points , we must multiply the numbers of the ...
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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 66 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 find the number formed found by multiplying given number given square greatest number hexagon 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 perpendicular proportion protractor quadrilateral radii radius equal ratio regular polygon right angle semi-circumference set intersecting side AC Solid Angles 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.