An Introduction to Geometry and the Science of Form: Prepared from the Most Approved Prussian Text-books |
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Page 18
... Multiply the number of lines by the same number less 1 , and divide this product by 2 . 2 = 23. We will now reverse the operation . Let us sup- pose the greatest number of points at which a certain number of straight lines can intersect ...
... Multiply the number of lines by the same number less 1 , and divide this product by 2 . 2 = 23. We will now reverse the operation . Let us sup- pose the greatest number of points at which a certain number of straight lines can intersect ...
Page 19
... number of lines which will give 45 points of intersection is 10 . 24. The intersecting straight lines may be divided ... Multiply the number of lines in one set by the number of lines in the other set , and add 2 to the product ...
... number of lines which will give 45 points of intersection is 10 . 24. The intersecting straight lines may be divided ... Multiply the number of lines in one set by the number of lines in the other set , and add 2 to the product ...
Page 20
... number of points , we must multiply the numbers of the two sets together and add 1 to the product . Example . Divide the number 16 into 2 sets as fol- lows , the 1st column being the number of lines in the set of parallels . 14 and 2 ...
... number of points , we must multiply the numbers of the two sets together and add 1 to the product . Example . Divide the number 16 into 2 sets as fol- lows , the 1st column being the number of lines in the set of parallels . 14 and 2 ...
Page 21
... number of points , and the lines of the other set intersecting one another at one point . In this case , first calculate the number of points in the first set ; then multiply the number of lines of the 2d set by the number of lines in ...
... number of points , and the lines of the other set intersecting one another at one point . In this case , first calculate the number of points in the first set ; then multiply the number of lines of the 2d set by the number of lines in ...
Page 24
... number of straight lines that can be drawn between 3 points is 3 X 2 2 3 . 3. Between 4 Points . Straight lines may ... Multiply the whole number of points by the same number less 1 , and divide the product by 2 . Between 7 points ...
... number of straight lines that can be drawn between 3 points is 3 X 2 2 3 . 3. Between 4 Points . Straight lines may ... Multiply the whole number of points by the same number less 1 , and divide the product by 2 . Between 7 points ...
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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 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.