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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Σελίδα 51
... radius BC , and producing DB the side of the equilateral triangle DBA to meet the circumference in G : next , with center D and radius DG , describing the circle GKL , and then producing DA to meet the circumference in L. By a similar ...
... radius BC , and producing DB the side of the equilateral triangle DBA to meet the circumference in G : next , with center D and radius DG , describing the circle GKL , and then producing DA to meet the circumference in L. By a similar ...
Σελίδα 53
... radius CD . " " Prop . XIV . is the converse of Prop . XIII . " Upon the opposite sides of it . ' If these words were omitted , it is possible for two lines to make with a third , two angles , which together are equal to two right ...
... radius CD . " " Prop . XIV . is the converse of Prop . XIII . " Upon the opposite sides of it . ' If these words were omitted , it is possible for two lines to make with a third , two angles , which together are equal to two right ...
Σελίδα 60
... radius . " How does this postulate differ from Euclid's , and which of his problems is assumed in it ? 17. What ... radius BC in two points G and H ; shew that either of the dis- tances DG , DH may be taken as the radius 60 EUCLID'S ...
... radius . " How does this postulate differ from Euclid's , and which of his problems is assumed in it ? 17. What ... radius BC in two points G and H ; shew that either of the dis- tances DG , DH may be taken as the radius 60 EUCLID'S ...
Σελίδα 61
... radius of the second circle ; and give the proof in each case . 36. Explain how the propositions Euc . 1. 2. 3 , are rendered necessary by the restriction imposed by the third postulate . Is it necessary for the proof , that the ...
... radius of the second circle ; and give the proof in each case . 36. Explain how the propositions Euc . 1. 2. 3 , are rendered necessary by the restriction imposed by the third postulate . Is it necessary for the proof , that the ...
Σελίδα 66
... radius equal to its distance from one of the given points , will 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 ...
... radius equal to its distance from one of the given points , will 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 ...
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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...