The Element of Geometry |
From inside the book
Results 1-5 of 46
Page 16
... Q. E. D. PROP . VIII . PROBLEM . To bisect a given finite straight line . Let AB be the given finite straight line ; it is required to bisect it . From A , with a radius ( Def . 50. ) AF greater than half AB , describe the arc DFE ...
... Q. E. D. PROP . VIII . PROBLEM . To bisect a given finite straight line . Let AB be the given finite straight line ; it is required to bisect it . From A , with a radius ( Def . 50. ) AF greater than half AB , describe the arc DFE ...
Page 18
... Q. E. D. PROP . XII . THEOR . If from the ends of the side of a 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 ...
... Q. E. D. PROP . XII . THEOR . If from the ends of the side of a 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 ...
Page 19
John Playfair. PROP . XIII . THEOR . If from a point without a straight line a perpendicular be ... Q. E. D. Cor . A perpendicular from a point to a straight line , measures the shortest distance between the point and the line . PROP ...
John Playfair. PROP . XIII . THEOR . If from a point without a straight line a perpendicular be ... Q. E. D. Cor . A perpendicular from a point to a straight line , measures the shortest distance between the point and the line . PROP ...
Page 28
... Q. E. D. PROP . IX . THEOR . The opposite sides and angles of a parallelogram are equal . In the quadrangle ABDC , lct AB be parallel to CD , and AC to BD . AB is equal to CD , and AC to BD . Join BC . Because AB is parallel to CD , and ...
... Q. E. D. PROP . IX . THEOR . The opposite sides and angles of a parallelogram are equal . In the quadrangle ABDC , lct AB be parallel to CD , and AC to BD . AB is equal to CD , and AC to BD . Join BC . Because AB is parallel to CD , and ...
Page 29
... Q. E. D. PROP . XI . THEOR . The perpendiculars between parallel lines are equal . Let AB and FD be parallel lines , and AC and BD perpendiculars between them ; AC is equal to BD . A B D Because the straight line FD falls on the ...
... Q. E. D. PROP . XI . THEOR . The perpendiculars between parallel lines are equal . Let AB and FD be parallel lines , and AC and BD perpendiculars between them ; AC is equal to BD . A B D Because the straight line FD falls on the ...
Other editions - View all
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...