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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Resultater 1-5 af 62
Side 2
... vertex of the angle , that is , at the point in which the straight lines that contain the angle meet one another , is put between the other two letters , and one of these two is somewhere upon one of these straight lines , and the other ...
... vertex of the angle , that is , at the point in which the straight lines that contain the angle meet one another , is put between the other two letters , and one of these two is somewhere upon one of these straight lines , and the other ...
Side 11
... vertex of each of the triangles is without the other triangle . Because AC is equal to AD in the triangle ACD , therefore the angle ADC is equal to the angle ACD ; ( 1. 5. ) but the angle ACD is greater than the angle BCD ; ( ax . 9 ...
... vertex of each of the triangles is without the other triangle . Because AC is equal to AD in the triangle ACD , therefore the angle ADC is equal to the angle ACD ; ( 1. 5. ) but the angle ACD is greater than the angle BCD ; ( ax . 9 ...
Side 12
... vertex of one triangle is upon a side of the other , needs no demonstration . Therefore , upon the same 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 ...
... vertex of one triangle is upon a side of the other , needs no demonstration . Therefore , upon the same 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 ...
Side 30
... vertex of all the triangles , are equal to four right angles , ( 1. 15. Cor . 2. ) therefore the same angles of these triangles are equal to the angles of the figure together with four right angles ; but it has been proved that the ...
... vertex of all the triangles , are equal to four right angles , ( 1. 15. Cor . 2. ) therefore the same angles of these triangles are equal to the angles of the figure together with four right angles ; but it has been proved that the ...
Side 44
... vertex of the angle , and must not be confounded with the magnitude of the angle itself . The right angle is fixed in mag- nitude , and , on this account , it is made the standard with which all other angles are compared . Two straight ...
... vertex of the angle , and must not be confounded with the magnitude of the angle itself . The right angle is fixed in mag- nitude , and , on this account , it is made the standard with which all other angles are compared . Two straight ...
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Almindelige termer og sætninger
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
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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...