The Element of Geometry |
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Page 11
... angles on one side of a straight line is equal to the sum of the an- gles on the other side . COR . II . Because a right angle is equal to half the sum of all the angles on one side of a straight line ( Def . 27. ) ; therefore all right ...
... angles on one side of a straight line is equal to the sum of the an- gles on the other side . COR . II . Because a right angle is equal to half the sum of all the angles on one side of a straight line ( Def . 27. ) ; therefore all right ...
Page 13
... DEF ; and the other angles , to which the equal sides are opposite , shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to the angle DFE . For , if the triangle ABC be applied to DEF , so that the ...
... DEF ; and the other angles , to which the equal sides are opposite , shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to the angle DFE . For , if the triangle ABC be applied to DEF , so that the ...
Page 15
... angle DBC is equal to the angle ACB ; therefore ( 4. 1. ) , the base DC is equal to the base AB , and the triangle ... DEF , have the three sides equal , that is , AB equal to DE , AC to DF , and BC to EF . The angles opposite the ...
... angle DBC is equal to the angle ACB ; therefore ( 4. 1. ) , the base DC is equal to the base AB , and the triangle ... DEF , have the three sides equal , that is , AB equal to DE , AC to DF , and BC to EF . The angles opposite the ...
Page 16
... angle GBC , or DEF , and the angle ACB to the angle GCB , or DFE . Therefore , if , & c . Q. E. D. PROP . VIII . PROBLEM . To bisect a given finite straight line . Let AB be the given finite straight line ; it is required to bisect ...
... angle GBC , or DEF , and the angle ACB to the angle GCB , or DFE . Therefore , if , & c . Q. E. D. PROP . VIII . PROBLEM . To bisect a given finite straight line . Let AB be the given finite straight line ; it is required to bisect ...
Page 17
... angles CDF , CEF are equal ; and therefore ( 4. 1. ) , the two triangles DFC , EFC are equivalent ; and the angle DCF is equal to the angle BCF , and therefore ( Def . 27. ) CF is perpendicular to DE , or AB . Wherefore , from the given ...
... angles CDF , CEF are equal ; and therefore ( 4. 1. ) , the two triangles DFC , EFC are equivalent ; and the angle DCF is equal to the angle BCF , and therefore ( Def . 27. ) CF is perpendicular to DE , or AB . Wherefore , from the given ...
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The Element of Geometry (Classic Reprint) Formerly Chairman Department of Immunology John Playfair,John Playfair No preview available - 2017 |
Common terms and phrases
AB is equal AC is equal adjacent angles angle ABC angle ACB angle BAC angle DEF arc AC base BC bisect called centre circle ABCD circle EFGH coincide described diameter divided drawn duplicate ratio equal angles equal circles equal to AC equiangular FGHKL fore four right angles given straight line gnomon greater homologous sides join less Let ABC Let the straight opposite angles parallel parallelogram perpendicular polygon PROB produced Q. E. D. PROP radius rectangle BC rectangle contained rectilineal figure remaining angle right angled triangle secant segment side AC similar sine square of AC straight line AB straight line AC THEOR touches the circle triangle ABC twice the rectangle wherefore whole angle
Popular passages
Page 25 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Page 13 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line E iR.
Page 4 - To draw a straight line at right angles to a given straight line, from a given point in the same.
Page 29 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...
Page 90 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Page 87 - ... magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there shall at length remain a magnitude less than the least of the proposed magnitudes.
Page 1 - If two triangles have two sides of the one equal to two sides of the...
Page 13 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Page 64 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Page 19 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...