The Element of Geometry |
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Page 85
... polygons have ; and the polygon ABCDE has to the polygon FGHKL the duplicate ratio of that which the side AB has to the side FG . Join BE , EC , GL , LH : and because the polygon ABCDE is similar to the polygon FGHKL , the angle BAE is ...
... polygons have ; and the polygon ABCDE has to the polygon FGHKL the duplicate ratio of that which the side AB has to the side FG . Join BE , EC , GL , LH : and because the polygon ABCDE is similar to the polygon FGHKL , the angle BAE is ...
Page 86
... polygon FGHKL the duplicate ratio of that which the side AB has to the homologous side FG . Because the triangle ABE ... polygon ABCDE to the polygon FGHKL ; but the triangle ABE has to the triangle FGL , the duplicate ratio of ...
... polygon FGHKL the duplicate ratio of that which the side AB has to the homologous side FG . Because the triangle ABE ... polygon ABCDE to the polygon FGHKL ; but the triangle ABE has to the triangle FGL , the duplicate ratio of ...
Page 87
... polygon upon FG like- wise the duplicate ratio of that which AB has to FG : therefore as AB is to M , so is the figure upon AB to the figure upon FG , which was also proved in triangles ( Cor . 19. 5. ) . Therefore , universally , it is ...
... polygon upon FG like- wise the duplicate ratio of that which AB has to FG : therefore as AB is to M , so is the figure upon AB to the figure upon FG , which was also proved in triangles ( Cor . 19. 5. ) . Therefore , universally , it is ...
Page 93
... polygon . IV . The sum of the sides of a figure may be called the perimeter of the figure . V. When the extremities of a straight line are in the circumference of a circle , the line may be said to be placed in the circle . PROPOSITION ...
... polygon . IV . The sum of the sides of a figure may be called the perimeter of the figure . V. When the extremities of a straight line are in the circumference of a circle , the line may be said to be placed in the circle . PROPOSITION ...
Page 97
... C. Q. E. D. B C E And if only the halves be taken away , the same thing may in the same way be demonstrated . PROP . VII . THEOR . Similar polygons inscribed in 13 OF GEOMETRY . BOOK VI . 97 , rallel to BED; therefore the figures GK, GC...
... C. Q. E. D. B C E And if only the halves be taken away , the same thing may in the same way be demonstrated . PROP . VII . THEOR . Similar polygons inscribed in 13 OF GEOMETRY . BOOK VI . 97 , rallel to BED; therefore the figures GK, GC...
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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...