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 44
... similar distinction of triangles . Def . xxx - XXXIV . The definitions of quadrilateral figures are liable to objection . All of them , except the trapezium , fall under the general idea of a parallelogram ; but as Euclid defined ...
... similar distinction of triangles . Def . xxx - XXXIV . The definitions of quadrilateral figures are liable to objection . All of them , except the trapezium , fall under the general idea of a parallelogram ; but as Euclid defined ...
Side 49
... similar way may be supplied the reserved premiss in every enthy- meme . The conclusion of two enthymemes may form the major and minor premiss of a third syllogism , and so on , and thus any process of reasoning is reduced to the ...
... similar way may be supplied the reserved premiss in every enthy- meme . The conclusion of two enthymemes may form the major and minor premiss of a third syllogism , and so on , and thus any process of reasoning is reduced to the ...
Side 51
... similar construction the less of two given straight lines may be produced , so that the less together with the part produced may be equal to the greater . Prop . III . This problem admits of two solutions , and it is left unde- termined ...
... similar construction the less of two given straight lines may be produced , so that the less together with the part produced may be equal to the greater . Prop . III . This problem admits of two solutions , and it is left unde- termined ...
Side 55
... similar way , it may be shewn that BC cannot be otherwise than equal to EF . If ACB , DFE be both right angles : the case falls under Euc . 1. 26 . Prop . XXVII . Alternate angles are defined to be the two angles which two straight ...
... similar way , it may be shewn that BC cannot be otherwise than equal to EF . If ACB , DFE be both right angles : the case falls under Euc . 1. 26 . Prop . XXVII . Alternate angles are defined to be the two angles which two straight ...
Side 61
... similar limitation necessary with respect to the three angles ? 52. Is it possible to form a triangle with three lines whose lengths are 1 , 2 , 3 units : or one with three lines whose lengths are 1 , √2 , √3 ? 53. Is it possible to ...
... similar limitation necessary with respect to the three angles ? 52. Is it possible to form a triangle with three lines whose lengths are 1 , 2 , 3 units : or one with three lines whose lengths are 1 , √2 , √3 ? 53. Is it possible to ...
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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.