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 σελίδες |
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Αποτελέσματα 1 - 5 από τα 83.
Σελίδα 7
... described upon the given straight line AB . Which was required to be done . PROPOSITION II . PROBLEM . 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 ...
... described upon the given straight line AB . Which was required to be done . PROPOSITION II . PROBLEM . 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 ...
Σελίδα 39
... described equal to the given rectilineal figure ABCD , having the angle FKM equal to the given angle E. Q. E. F. COR . From this it is manifest how , to a given stright line , to apply a parallelogram , which shall have an angle equal ...
... described equal to the given rectilineal figure ABCD , having the angle FKM equal to the given angle E. Q. E. F. COR . From this it is manifest how , to a given stright line , to apply a parallelogram , which shall have an angle equal ...
Σελίδα 40
... described upon the side subtending the right angle , is equal to the squares described upon the sides which contain the right angle . Let ABC be a right - angled triangle , having the right angle BAC . Then the square described upon the ...
... described upon the side subtending the right angle , is equal to the squares described upon the sides which contain the right angle . Let ABC be a right - angled triangle , having the right angle BAC . Then the square described upon the ...
Σελίδα 41
... described upon one of the sides of a triangle , be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle . Let the square described upon BC , one of the sides of the ...
... described upon one of the sides of a triangle , be equal to the squares described upon the other two sides of it ; the angle contained by these two sides is a right angle . Let the square described upon BC , one of the sides of the ...
Σελίδα 42
... described by a proper term or terms , does not in fact admit of definition properly so called . The definitions in Euclid's Elements may be divided into two classes , those which merely explain the meaning of the terms employed , and ...
... described by a proper term or terms , does not in fact admit of definition properly so called . The definitions in Euclid's Elements may be divided into two classes , those which merely explain the meaning of the terms employed , and ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 26 - ... upon the same side together equal to two right angles, the two straight lines shall be parallel to one another.
Σελίδα 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.
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 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...
Σελίδα 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.
Σελίδα 67 - A proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate or capable of innumerable solutions.