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 9
... base BC shall coincide with the base EF ; because the point B coinciding with E , and C with F , if the base BC do not coincide with the base EF , the two straight lines BC and EF would enclose a space , which is impossible . ( ax . 10 ...
... base BC shall coincide with the base EF ; because the point B coinciding with E , and C with F , if the base BC do not coincide with the base EF , the two straight lines BC and EF would enclose a space , which is impossible . ( ax . 10 ...
Página 10
... base FC is equal to the base GB , ( 1. 4. ) and the triangle AFC is equal to the triangle AGB , also the remaining angles of the one are equal to the remaining angles of the other , each to each , to which the equal sides are opposite ...
... base FC is equal to the base GB , ( 1. 4. ) and the triangle AFC is equal to the triangle AGB , also the remaining angles of the one are equal to the remaining angles of the other , each to each , to which the equal sides are opposite ...
Página 11
... base DC is equal to the base AB , ( 1. 4. ) and the triangle DBC is equal to the triangle ABC , the less equal to the greater , which is absurd . ( ax . 9. ) Therefore AB is not unequal to AC , that is , AB is equal to AC . Wherefore ...
... base DC is equal to the base AB , ( 1. 4. ) and the triangle DBC is equal to the triangle ABC , the less equal to the greater , which is absurd . ( ax . 9. ) Therefore AB is not unequal to AC , that is , AB is equal to AC . Wherefore ...
Página 12
... base and on the same side of it , & c . Q.E.D. PROPOSITION VIII . THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; the angle which is con- tained ...
... base and on the same side of it , & c . Q.E.D. PROPOSITION VIII . THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; the angle which is con- tained ...
Página 13
... base DF is equal to the base EF : ( constr . ) therefore the angle DAF is equal to the angle EAF . ( 1.8 . ) Wherefore the angle BAC is bisected by the straight line AF . Q.E.F. PROPOSITION X. PROBLEM . To bisect a given finite straight ...
... base DF is equal to the base EF : ( constr . ) therefore the angle DAF is equal to the angle EAF . ( 1.8 . ) Wherefore the angle BAC is bisected by the straight line AF . Q.E.F. PROPOSITION X. PROBLEM . To bisect a given finite straight ...
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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...