Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes .... the first six booksJ. W. Parker & son, 1860 - 361 Seiten |
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Seite 10
... proved to be equal to GB ; hence , because the two sides BF , FC are equal to the two CG , GB , each to each ; and the angle BFC has been proved to be equal to the angle CGB , also the base BC is common to the two triangles BFC , CGB ...
... proved to be equal to GB ; hence , because the two sides BF , FC are equal to the two CG , GB , each to each ; and the angle BFC has been proved to be equal to the angle CGB , also the base BC is common to the two triangles BFC , CGB ...
Seite 12
... proved greater than BCD , 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 ...
... proved greater than BCD , 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 ...
Seite 16
... proved equal to the same three angles ; and things which are equal to the same thing are equal to one another ; therefore the angles CBE , EBD are equal to the angles DBA , ABC ; but the angles CBE , EBD are two right angles ; therefore ...
... proved equal to the same three angles ; and things which are equal to the same thing are equal to one another ; therefore the angles CBE , EBD are equal to the angles DBA , ABC ; but the angles CBE , EBD are two right angles ; therefore ...
Seite 19
... proved equal to the angle ABD , therefore the angle ABD is greater than the angle DCB ; 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 ...
... proved equal to the angle ABD , therefore the angle ABD is greater than the angle DCB ; 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 ...
Seite 23
... proved equal to BC ; therefore BC is greater than EF . 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 ...
... proved equal to BC ; therefore BC is greater than EF . 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 ...
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 54 - If two triangles have two sides of the one equal to two sides of the...
Seite 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...
Seite 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.
Seite 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.
Seite 18 - Any two angles of a triangle are together less than two right angles.
Seite 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.
Seite 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.
Seite 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.
Seite 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Seite 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...