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
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC . ( ax . 1. ) Wherefore from the given point A , a straight line AL ...
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC . ( ax . 1. ) Wherefore from the given point A , a straight line AL ...
Página 9
... wherefore the 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 ...
... wherefore the 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 ...
Página 12
... wherefore the angle BDC is both equal to , and greater than the angle BCD ; which is impossible . Thirdly . The case in which the vertex of one triangle is upon a side of the other , needs no demonstration . Therefore , upon the same ...
... wherefore the angle BDC is both equal to , and greater than the angle BCD ; which is impossible . Thirdly . The case in which the vertex of one triangle is upon a side of the other , needs no demonstration . Therefore , upon the same ...
Página 13
... Wherefore the angle BAC is bisected by the straight line AF . Q.E.F. PROPOSITION X. PROBLEM . To bisect a given finite straight line , that is , to divide it into two equal parts . Let AB be the given straight line . It is required to ...
... Wherefore the angle BAC is bisected by the straight line AF . Q.E.F. PROPOSITION X. PROBLEM . To bisect a given finite straight line , that is , to divide it into two equal parts . Let AB be the given straight line . It is required to ...
Página 14
... Wherefore from the given point C , in the given straight line AB , FC has been drawn at right angles to AB . Q.E.F. COR . By help of this problem , it may be demonstrated that two straight lines cannot have a common segment . If it be ...
... Wherefore from the given point C , in the given straight line AB , FC has been drawn at right angles to AB . Q.E.F. COR . By help of this problem , it may be demonstrated that two straight lines cannot have a common segment . If it be ...
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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...