The Element of Geometry |
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Page 11
... angles made by one of the lines is equal to the sum of the angles made by the other . From the points C and Gin the ... adjacent angles together equal to two right an- gles , these two straight lines shall be in the same straight ...
... angles made by one of the lines is equal to the sum of the angles made by the other . From the points C and Gin the ... adjacent angles together equal to two right an- gles , these two straight lines shall be in the same straight ...
Page 12
... adjacent angles together equal to two right angles , these two straight lines shall be in the same straight line . Which was to be proved . PROP . III . THEOR . If two straight lines cut one another , the vertical or opposite angles ...
... adjacent angles together equal to two right angles , these two straight lines shall be in the same straight line . Which was to be proved . PROP . III . THEOR . If two straight lines cut one another , the vertical or opposite angles ...
Page 17
... angles CDF , CEF are equal ; and therefore ( 4. 1. ) , the two triangles DFC , EFC are equivalent ; and the angle ... adjacent angles ; but when a straight line , standing on a straight line , makes the adjacent angles equal to one ...
... angles CDF , CEF are equal ; and therefore ( 4. 1. ) , the two triangles DFC , EFC are equivalent ; and the angle ... adjacent angles ; but when a straight line , standing on a straight line , makes the adjacent angles equal to one ...
Page 18
... adjacent angles equal to two right angles , these two straight lines shall be in the same straight line ( 2. 1. ) ; therefore ACF is a straight line ; and between the points A and F there are two straight lines which do not coincide ...
... adjacent angles equal to two right angles , these two straight lines shall be in the same straight line ( 2. 1. ) ; therefore ACF is a straight line ; and between the points A and F there are two straight lines which do not coincide ...
Page 34
... adjacent angles equal to two right angles ; therefore AC is in the same straight line ( 2.1 . ) with AG : for the same reason , AB and AH are in the same straight line ; and because the angle DBC is equal to the angle FBA , each of them ...
... adjacent angles equal to two right angles ; therefore AC is in the same straight line ( 2.1 . ) with AG : for the same reason , AB and AH are in the same straight line ; and because the angle DBC is equal to the angle FBA , each of them ...
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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...