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 16
... Wherefore , when a straight line , & c . Q.E.D. PROPOSITION XIV . THEOREM . If at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles ; then ...
... Wherefore , when a straight line , & c . Q.E.D. PROPOSITION XIV . THEOREM . If at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles ; then ...
Página 19
... wherefore much more is the angle ABC greater than the angle ACB . Therefore the greater side , & c . Q.E.D. PROPOSITION XIX . THEOREM . The greater angle of every triangle is subtended by the greater side , or , has the greater side ...
... wherefore much more is the angle ABC greater than the angle ACB . Therefore the greater side , & c . Q.E.D. PROPOSITION XIX . THEOREM . The greater angle of every triangle is subtended by the greater side , or , has the greater side ...
Página 22
... Wherefore , at the given point A in the given straight line AB , the angle FAG is made equal to the given rectilineal angle DCE . Q.E.F. PROPOSITION XXIV . THEOREM . If two triangles have two sides of the one equal to two sides of the ...
... Wherefore , at the given point A in the given straight line AB , the angle FAG is made equal to the given rectilineal angle DCE . Q.E.F. PROPOSITION XXIV . THEOREM . If two triangles have two sides of the one equal to two sides of the ...
Página 23
... Wherefore , if two triangles , & c . Q.E.D. PROPOSITION XXV . THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each , but the base of one greater than the base of the other ; the angle ...
... Wherefore , if two triangles , & c . Q.E.D. PROPOSITION XXV . THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each , but the base of one greater than the base of the other ; the angle ...
Página 25
... wherefore BC is not unequal to EF , that is , BC is equal to EF . Hence , in the triangles ABC , DEF ; because AB is ... Wherefore , if two triangles , & c . Q. E. D. PROPOSITION XXVII . THEOREM . If a straight line falling on two other ...
... wherefore BC is not unequal to EF , that is , BC is equal to EF . Hence , in the triangles ABC , DEF ; because AB is ... Wherefore , if two triangles , & c . Q. E. D. PROPOSITION XXVII . THEOREM . If a straight line falling on two other ...
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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...