Elements of Geometry |
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Page iii
... figures are large and distinct , and are placed in the middle of the page , so that they fall directly under the eye in imme- diate connection with the corresponding text . The given lines of the figures are full lines , the lines employed.
... figures are large and distinct , and are placed in the middle of the page , so that they fall directly under the eye in imme- diate connection with the corresponding text . The given lines of the figures are full lines , the lines employed.
Page iv
... given is printed in one kind of type , of what is required in another , and the demonstration in still another . The reason for each step is indicated in small type between that step and the one follow- ing , thus preventing the ...
... given is printed in one kind of type , of what is required in another , and the demonstration in still another . The reason for each step is indicated in small type between that step and the one follow- ing , thus preventing the ...
Page vi
... given by multiplying a constant into the approximate values of any repetend . If , for exam- ple , we take the constant 60 and the repetend .3333 , etc. , the approxi- mate values of the repetend will be 10 , 100 , 1000 , 108000 , etc ...
... given by multiplying a constant into the approximate values of any repetend . If , for exam- ple , we take the constant 60 and the repetend .3333 , etc. , the approxi- mate values of the repetend will be 10 , 100 , 1000 , 108000 , etc ...
Page 7
... given line . Thus , if A B = BC CD , etc. , AB DE , then AC = 2 AB , AD = = 3 A B , etc. А В + C + - It must also be possible to divide a given straight line into an assigned number of equal parts . For , assumed that the nth part of a ...
... given line . Thus , if A B = BC CD , etc. , AB DE , then AC = 2 AB , AD = = 3 A B , etc. А В + C + - It must also be possible to divide a given straight line into an assigned number of equal parts . For , assumed that the nth part of a ...
Page 9
... angle is the difference between a right angle and the given angle . Thus ABD is the complement of the angle DBC ; also DBC is the com- plement of the angle A B D. A D B 31. DEF . The Supplement of an angle is the DEFINITIONS . 9.
... angle is the difference between a right angle and the given angle . Thus ABD is the complement of the angle DBC ; also DBC is the com- plement of the angle A B D. A D B 31. DEF . The Supplement of an angle is the DEFINITIONS . 9.
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Common terms and phrases
A B C D AABC AACB AB² ABCD adjacent angles apothem arc A B base and altitude BC² centre centre of symmetry circumference circumscribed construct a square COROLLARY decagon diagonals diameter divided Draw equal arcs equal distances equal respectively equiangular equiangular polygon equilateral equilateral polygon exterior angles figure given circle given line given polygon given square homologous sides hypotenuse intersecting isosceles Let A B Let ABC line A B measured by arc middle point number of sides parallelogram perpendicular plane polygon ABC polygon similar PROBLEM prove Q. E. D. PROPOSITION quadrilateral radii radius equal ratio rect rectangles regular inscribed regular polygon required to construct right angles right triangle SCHOLIUM segment semicircle similar polygons subtend symmetrical with respect tangent THEOREM triangle ABC vertex vertices
Popular passages
Page 40 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Page 126 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Page 136 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Page 207 - Construct a rectangle having the difference of its base and altitude equal to a given line, and its area equivalent to the sum of a given triangle and a given pentagon.
Page 202 - In any proportion, the product of the means is equal to the product of the extremes.
Page 142 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Page 175 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 72 - Every point in the bisector of an angle is equally distant from the sides of the angle ; and every point not in the bisector, but within the angle, is unequally distant from the sides of the angle.
Page 73 - A CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Page 146 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.