Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes .... the first six booksJ. W. Parker & son, 1860 - 361 sider |
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Side 8
... angles contained by those sides equal to each other ; they shall likewise have their bases or third sides equal , and the two ... BAC equal to the included angle EDF . Then shall the base BC be equal to the base 8 EUCLID'S ELEMENTS .
... angles contained by those sides equal to each other ; they shall likewise have their bases or third sides equal , and the two ... BAC equal to the included angle EDF . Then shall the base BC be equal to the base 8 EUCLID'S ELEMENTS .
Side 9
... angle BAC is equal to the angle EDF ; therefore also the point C shall coincide with the point F , because AC is equal to DF ; but the point B was shewn to coincide with the point E ; wherefore the base BC shall coincide with the base ...
... angle BAC is equal to the angle EDF ; therefore also the point C shall coincide with the point F , because AC is equal to DF ; but the point B was shewn to coincide with the point E ; wherefore the base BC shall coincide with the base ...
Side 12
... angle ECD is greater than the angle BCD ; ( ax . 9. ) therefore also the angle FDC is greater than the angle BCD ... BAC shall be equal to the angle EDF . For , if the triangle ABC be applied to DEF , so that the point B be on E , and ...
... angle ECD is greater than the angle BCD ; ( ax . 9. ) therefore also the angle FDC is greater than the angle BCD ... BAC shall be equal to the angle EDF . For , if the triangle ABC be applied to DEF , so that the point B be on E , and ...
Side 13
... angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle . It is required to bisect it . D A A B F In AB take any point D ; from AC cut off AE equal to AD , ( 1. 3. ) and join DE , on the side of DE ...
... angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle . It is required to bisect it . D A A B F In AB take any point D ; from AC cut off AE equal to AD , ( 1. 3. ) and join DE , on the side of DE ...
Side 17
... angles shall be equal . Let the two straight lines AB , CD cut one another in the point E. Then the angle AEC shall ... BAC . F A. B G Bisect AC in E , ( 1. 10. ) and join BE ; produce BE to F , making EF equal to BE , ( 1. 3. ) and join ...
... angles shall be equal . Let the two straight lines AB , CD cut one another in the point E. Then the angle AEC shall ... BAC . F A. B G Bisect AC in E , ( 1. 10. ) and join BE ; produce BE to F , making EF equal to BE , ( 1. 3. ) and join ...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ... Robert Potts Uten tilgangsbegrensning - 1845 |
Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson with ... Euclid,Robert Potts Uten tilgangsbegrensning - 1847 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 54 - If two triangles have two sides of the one equal to two sides of the...
Side 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...
Side 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.
Side 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.
Side 18 - Any two angles of a triangle are together less than two right angles.
Side 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.
Side 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.
Side 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.
Side 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 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...