The Element of Geometry |
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Page 13
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal , each to each , viz . the angle ...
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal , each to each , viz . the angle ...
Page 15
... angles opposite the equal sides shall also be equal ; that is , the angle BAC to the an- gle EDF , ABC to DEF , and ACB to DFE . Let the triangles be joined by the longest equal sides BC and EF , having the remaining sides GB equal to ...
... angles opposite the equal sides shall also be equal ; that is , the angle BAC to the an- gle EDF , ABC to DEF , and ACB to DFE . Let the triangles be joined by the longest equal sides BC and EF , having the remaining sides GB equal to ...
Page 25
... angle DAE equal to the angle ADC ; and produce the straight line AE to F. Because the straight line AD , falling on ... BAC , ACE are equal ( 3.2 . ) . Again , because AB is parallel to CE , and BD falls upon them 4 OF GEOMETRY ...
... angle DAE equal to the angle ADC ; and produce the straight line AE to F. Because the straight line AD , falling on ... BAC , ACE are equal ( 3.2 . ) . Again , because AB is parallel to CE , and BD falls upon them 4 OF GEOMETRY ...
Page 26
... angle BAC ; therefore the whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC : to these equals add the angle ACB , and the angles ACD , ACB are equal to the three an- gles CBA , BAC , ACB ; but the ...
... angle BAC ; therefore the whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC : to these equals add the angle ACB , and the angles ACD , ACB are equal to the three an- gles CBA , BAC , ACB ; but the ...
Page 27
... angles in each of the triangles ABC , DEF , are equal to two right angles ( 5. 2. ) , they are equal to each other ; take away the angles ABC , BCA , equal to the angles DEF , EFD , and the remaining angle BAC will be equal to the remaining ...
... angles in each of the triangles ABC , DEF , are equal to two right angles ( 5. 2. ) , they are equal to each other ; take away the angles ABC , BCA , equal to the angles DEF , EFD , and the remaining angle BAC will be equal to the remaining ...
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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...