Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Explanatory Notes .... the first six booksJ. W. Parker & son, 1860 - 361 σελίδες |
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Αποτελέσματα 1 - 5 από τα 68.
Σελίδα 36
... passes : also BK , KD the other parallelograms which make up the whole figure ABCD , which are therefore called the complements . Then the complement BK shall be equal to the complement KD . E A H D K F B G C Because 36 EUCLID'S ELEMENTS .
... passes : also BK , KD the other parallelograms which make up the whole figure ABCD , which are therefore called the complements . Then the complement BK shall be equal to the complement KD . E A H D K F B G C Because 36 EUCLID'S ELEMENTS .
Σελίδα 66
... pass through the other point , and the perpendicular will be the locus of all the circles which can be described passing through the two given points . Again , if a third point C be taken , but not in the same straight line with the ...
... pass through the other point , and the perpendicular will be the locus of all the circles which can be described passing through the two given points . Again , if a third point C be taken , but not in the same straight line with the ...
Σελίδα 77
... passes through A. 48. In a triangle ABC , AD being drawn perpendicular to the straight line BD which bisects the angle B , shew that a line drawn from D parallel to BC will bisect AC . 49. If the sides of a triangle be trisected and ...
... passes through A. 48. In a triangle ABC , AD being drawn perpendicular to the straight line BD which bisects the angle B , shew that a line drawn from D parallel to BC will bisect AC . 49. If the sides of a triangle be trisected and ...
Σελίδα 78
... pass through two given points and have its base on a given straight line . 66. Construct an equilateral triangle , having given the length of the perpendicular drawn from one of the angles on the opposite side . 67. Having given the ...
... pass through two given points and have its base on a given straight line . 66. Construct an equilateral triangle , having given the length of the perpendicular drawn from one of the angles on the opposite side . 67. Having given the ...
Σελίδα 81
... pass through a given point , the least is that whose base is bisected in the given point . 111. Of all triangles having the same base and the same perimeter , that is the greatest which has the two undetermined sides equal . 112. Divide ...
... pass through a given point , the least is that whose base is bisected in the given point . 111. Of all triangles having the same base and the same perimeter , that is the greatest which has the two undetermined sides equal . 112. Divide ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 54 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 18 - Any two angles of a triangle are together less than two right angles.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 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...