The Element of Geometry |
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Page 36
... square of the whole line is equal to the squares of the two parts , together with twice the rectangle contained by the parts . Let the straight line AB be divided into any two parts in C ; the square of AB is equal to the squares of AC ...
... square of the whole line is equal to the squares of the two parts , together with twice the rectangle contained by the parts . Let the straight line AB be divided into any two parts in C ; the square of AB is equal to the squares of AC ...
Page 40
... rectangle CF , FA , together with the square of AE , is equal to the squares of BA , AE : take A F G H B away the ... twice the rectangle contained by the whole and that part , together with the square of the other part . Let the ...
... rectangle CF , FA , together with the square of AE , is equal to the squares of BA , AE : take A F G H B away the ... twice the rectangle contained by the whole and that part , together with the square of the other part . Let the ...
Page 41
... twice the rectangle AB , BC , together with the square AC . Wherefore , if a straight line , & c . Q. E. D. PROP . XXVI . THEOR . In obtuse angled triangles , if a perpendicular be drawn from any of the acute angles to the opposite side ...
... twice the rectangle AB , BC , together with the square AC . Wherefore , if a straight line , & c . Q. E. D. PROP . XXVI . THEOR . In obtuse angled triangles , if a perpendicular be drawn from any of the acute angles to the opposite side ...
Page 42
... twice the rectangle contained by CB , BD , and the square of DC : to each of these equals add the square of AD ; therefore the squares of CB , BD , DA are equal to twice the rectangle CB BD , and the squares of AD , DC : but the B square ...
... twice the rectangle contained by CB , BD , and the square of DC : to each of these equals add the square of AD ; therefore the squares of CB , BD , DA are equal to twice the rectangle CB BD , and the squares of AD , DC : but the B square ...
Page 108
... triangle , & c . Q. E. D. PROP . V. In any triangle , twice the rectangle contained by any two sides is to the difference of the sum of the squares of these two sides , and the square of the base , as the radius is to the co - sine of ...
... triangle , & c . Q. E. D. PROP . V. In any triangle , twice the rectangle contained by any two sides is to the difference of the sum of the squares of these two sides , and the square of the base , as the radius is to the co - sine of ...
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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...