Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes .... the first six booksJ. W. Parker & son, 1860 - 361 páginas |
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Página 8
... greater . It is required to cut off from AB the greater , a part equal to C , the less . D F EB From the point A draw the straight line AD equal to C ; ( 1. 2. ) and from the center A , at the distance AD , describe the circle DEF ...
... greater . It is required to cut off from AB the greater , a part equal to C , the less . D F EB From the point A draw the straight line AD equal to C ; ( 1. 2. ) and from the center A , at the distance AD , describe the circle DEF ...
Página 11
... greater than the other . If possible , let AB be greater than AC ; and from BA cut off BD equal to CA the less , ( I. 3. ) and join DC . Then , in the triangles DBC , ABC , because DB is equal to AC , and BC is common to both triangles ...
... greater than the other . If possible , let AB be greater than AC ; and from BA cut off BD equal to CA the less , ( I. 3. ) and join DC . Then , in the triangles DBC , ABC , because DB is equal to AC , and BC is common to both triangles ...
Página 12
... greater than the angle BCD ; ( ax . 9. ) therefore also the angle FDC is greater than the angle BCD ; much more then is the angle BDC greater than the angle BCD . Again , because BC is equal to BD in the triangle BCD , therefore the ...
... greater than the angle BCD ; ( ax . 9. ) therefore also the angle FDC is greater than the angle BCD ; much more then is the angle BDC greater than the angle BCD . Again , because BC is equal to BD in the triangle BCD , therefore the ...
Página 17
... greater than either of the interior opposite angles . Let ABC be a triangle , and let the side BC be produced to D. Then the exterior angle ACD shall be greater than either of the interior opposite angles CBA or BAC . F A. B G Bisect AC ...
... greater than either of the interior opposite angles . Let ABC be a triangle , and let the side BC be produced to D. Then the exterior angle ACD shall be greater than either of the interior opposite angles CBA or BAC . F A. B G Bisect AC ...
Página 18
... greater than the angle ECF ; therefore the angle ACD is greater than the angle BAE or BAC . In the same manner , if the side BC be bisected , and AC be pro- duced to G ; it may be demonstrated that the angle BCG , that is , the angle ...
... greater than the angle ECF ; therefore the angle ACD is greater than the angle BAE or BAC . In the same manner , if the side BC be bisected , and AC be pro- duced to G ; it may be demonstrated that the angle BCG , that is , the angle ...
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Términos y frases comunes
A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC Apply Euc axiom base BC chord circle ABC constr describe a circle diagonals diameter divided double draw equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements exterior angle Geometrical given circle given line given point given straight line given triangle gnomon greater hypotenuse inscribed intersection isosceles triangle less Let ABC line AC lines be drawn meet the circumference multiple opposite angles parallelogram pentagon perpendicular porism problem produced Prop proportionals proved Q.E.D. PROPOSITION quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar similar triangles square on AC tangent THEOREM touch the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
Pasajes populares
Página 54 - If two triangles have two sides of the one equal to two sides of the...
Página 89 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Página 38 - Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.
Página 144 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Página 18 - Any two angles of a triangle are together less than two right angles.
Página 266 - 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.
Página 152 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Página 7 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line; it is required to draw from the point A a straight line equal to BC.
Página 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 96 - 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...