The Element of Geometry |
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Page 15
... reason , in the triangle ACG the angle CAG is equal to the angle CGA ; and therefore , the two angles BAG and A B E F CAG , or BAC , are equal to the two angles BGA and CGA , or BGC ; then the triangles ABC , GBC have the two AB , AC ...
... reason , in the triangle ACG the angle CAG is equal to the angle CGA ; and therefore , the two angles BAG and A B E F CAG , or BAC , are equal to the two angles BGA and CGA , or BGC ; then the triangles ABC , GBC have the two AB , AC ...
Page 23
... reason , the angles GHF and GHE are together equal to two right an- gles ; take away the equal angles AGD and GHF , and the remainder AGC is equal to the remainder GHE : and because AGC and DGH are vertical angles , they are equal ( 3 ...
... reason , the angles GHF and GHE are together equal to two right an- gles ; take away the equal angles AGD and GHF , and the remainder AGC is equal to the remainder GHE : and because AGC and DGH are vertical angles , they are equal ( 3 ...
Page 32
... reason EF coincides with AF . And because ABCD is a parallelogram , AD is equal to BC ( 9.2 . ) . For the same reason , EF is equal to BC , and AD being equal to EF , and DE common , the whole or the remainder AE is equal to the whole ...
... reason EF coincides with AF . And because ABCD is a parallelogram , AD is equal to BC ( 9.2 . ) . For the same reason , EF is equal to BC , and AD being equal to EF , and DE common , the whole or the remainder AE is equal to the whole ...
Page 34
... reason , AB and AH are in the same straight line ; and because the angle DBC is equal to the angle FBA , each of them being a right angle ( Def . 5. 2. ) , add to each the angle ABC , and the whole angle DBA is equal to the whole FBC ...
... reason , AB and AH are in the same straight line ; and because the angle DBC is equal to the angle FBA , each of them being a right angle ( Def . 5. 2. ) , add to each the angle ABC , and the whole angle DBA is equal to the whole FBC ...
Page 35
... reason , the triangle KGC is equal to the triangle KFC , then , because the triangle AEK is equal to the triangle AHK , and the triangle KGC equal to the triangle KFC ; the triangle AEK , together with the tri- angle KGC , is equal to ...
... reason , the triangle KGC is equal to the triangle KFC , then , because the triangle AEK is equal to the triangle AHK , and the triangle KGC equal to the triangle KFC ; the triangle AEK , together with the tri- angle KGC , is equal to ...
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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 divided drawn duplicate ratio equal 17 equal angles equal circles equal to CD 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...