The Element of Geometry |
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Page 13
... 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 ABC to the angle DEF , and the angle ACB to the angle DFE . For , if the triangle ABC be ...
... 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 ABC to the angle DEF , and the angle ACB to the angle DFE . For , if the triangle ABC be ...
Page 14
... triangle ACF is equivalent to the triangle ABG ; and therefore the angle AFC is equal to the angle AGB : and because ... ABC is therefore equal to the remaining angle ACB , which are the angles at the base of the tri- angle ABC ...
... triangle ACF is equivalent to the triangle ABG ; and therefore the angle AFC is equal to the angle AGB : and because ... ABC is therefore equal to the remaining angle ACB , which are the angles at the base of the tri- angle ABC ...
Page 15
... triangle is also equilateral . PROP . VII . THEOR . If two triangles have the three sides of the one equal to the three sides of the other , each to each ; the angles opposite the equal sides are also equal . Let the two triangles ABC ...
... triangle is also equilateral . PROP . VII . THEOR . If two triangles have the three sides of the one equal to the three sides of the other , each to each ; the angles opposite the equal sides are also equal . Let the two triangles ABC ...
Page 18
... triangle there be drawn two straight lines to a point within the triangle , these shall be less than the other two sides of the triangle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC ...
... triangle there be drawn two straight lines to a point within the triangle , these shall be less than the other two sides of the triangle . Let the two straight lines BD , CD be drawn from B , C , the ends of the side BC of the triangle ABC ...
Page 19
... triangles ABC , ABE have the side BC equal to the side BE , the side AB common , and the contained angle ABC equal to the contained angle ABE , being both right angles by the hypothe- sis , ( Cor . 2. 1. ) , the triangles are equivalent ...
... triangles ABC , ABE have the side BC equal to the side BE , the side AB common , and the contained angle ABC equal to the contained angle ABE , being both right angles by the hypothe- sis , ( Cor . 2. 1. ) , the triangles are equivalent ...
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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...