Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with Appendix by Thos. Kirkland. the first six booksA. Miller & Company, 1876 - 403 sider |
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Side
... means of developing and cultivating the reason : and that " the object of a liberal education is to develope the whole mental system of man ; -to make his speculative inferences coincide with his practical convictions ; -to enable him ...
... means of developing and cultivating the reason : and that " the object of a liberal education is to develope the whole mental system of man ; -to make his speculative inferences coincide with his practical convictions ; -to enable him ...
Side
... meaning and a reality to the best attempts to explain man's power of arriving at truth . Other branches of Mathematics have , in like manner , become recognized examples , among educated men , of man's powers of attaining truth . " Dr ...
... meaning and a reality to the best attempts to explain man's power of arriving at truth . Other branches of Mathematics have , in like manner , become recognized examples , among educated men , of man's powers of attaining truth . " Dr ...
Side 42
... meaning of the terms , suppose the existence of the things described in the definitions . Definitions in Geometry ... means , a visible sign or mark on a surface , in other words , a physical point . The English term point , means the ...
... meaning of the terms , suppose the existence of the things described in the definitions . Definitions in Geometry ... means , a visible sign or mark on a surface , in other words , a physical point . The English term point , means the ...
Side 43
... meaning of the definition of a point : and we may add , that , in the Elements , Euclid supposes that the intersection ... mean , that no part of the line which is called a straight line deviates either from one side or the other of the ...
... meaning of the definition of a point : and we may add , that , in the Elements , Euclid supposes that the intersection ... mean , that no part of the line which is called a straight line deviates either from one side or the other of the ...
Side 44
... meaning of the term angulus suggests the Geometrical conception of an angle , which may be regarded as formed by the divergence of two straight lines from a point . In the definition of an angle , the magnitude of the angle is ...
... meaning of the term angulus suggests the Geometrical conception of an angle , which may be regarded as formed by the divergence of two straight lines from a point . In the definition of an angle , the magnitude of the angle is ...
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Vanlige uttrykk og setninger
A₁ ABCD AC is equal Algebraically angle ABC angle ACB angle BAC angle equal Apply Euc base BC chord circle ABC constr describe a circle diagonals diameter divided draw equal angles equiangular equilateral triangle equimultiples Euclid exterior angle Geometrical given circle given line given point given straight line gnomon greater hypotenuse inscribed intersection isosceles triangle less Let ABC line BC lines be drawn multiple opposite angles parallelogram parallelopiped pentagon perpendicular plane polygon produced Prop proportionals proved Q.E.D. PROPOSITION quadrilateral quadrilateral figure radius ratio rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar similar triangles solid angle square on AC tangent THEOREM touch the circle triangle ABC twice the rectangle vertex vertical angle wherefore
Populære avsnitt
Side 93 - If a straight line be bisected and produced to any point, the square on the whole line thus produced, and the square on the part of it produced, are together double of the square on half the line bisected, and of the square on the line made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to D ; The squares on AD and DB shall be together double of the squares on AC and CD. CONSTRUCTION. — From the point C draw CE at right angles to AB, and make it equal...
Side 118 - Guido, with a burnt stick in his hand, demonstrating on the smooth paving-stones of the path, that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.
Side 145 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Side 88 - If a straight line be divided into two equal parts and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Side 26 - ... upon the same side together equal to two right angles, the two straight lines shall be parallel to one another.
Side 36 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
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 92 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts...
Side xv - In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Side 67 - A proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate or capable of innumerable solutions.