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 ... whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it ; and the other angles of ...
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle ... whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it ; and the other angles of ...
Page 14
... angle AFC is equal to the angle AGB : and because the whole AF is equal to the whole AG , of which the parts AB , AC are equal ; the remainder BF shall be equal to the remainder CG ; but CF is equal ( 4. 1. ) to BG ; therefore , the two ...
... angle AFC is equal to the angle AGB : and because the whole AF is equal to the whole AG , of which the parts AB , AC are equal ; the remainder BF shall be equal to the remainder CG ; but CF is equal ( 4. 1. ) to BG ; therefore , the two ...
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 29
... whole angle ABD is equal to the whole angle ACD ; and the angle BAC has been shown to be equal to the angle BDC . Therefore , & c . Cor . Because the triangles ABC , BCD are equivalent , as proved above ; therefore the diagonal bisects ...
... whole angle ABD is equal to the whole angle ACD ; and the angle BAC has been shown to be equal to the angle BDC . Therefore , & c . Cor . Because the triangles ABC , BCD are equivalent , as proved above ; therefore the diagonal bisects ...
Page 32
... whole or the remainder DF . AB is also equal to AC , and the two EB , AB , are equal to the two , FD , DC , each to each ; and the angle FDC is equal to the angle EAB , because they are corresponding angles ( 3. 2. ) ; therefore the ...
... whole or the remainder DF . AB is also equal to AC , and the two EB , AB , are equal to the two , FD , DC , each to each ; and the angle FDC is equal to the angle EAB , because they are corresponding angles ( 3. 2. ) ; therefore the ...
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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...