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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Σελίδα 2
... contained by AB , DB , is named the angle ABD , or DBA ; and that which is contained by DB , CB , is called the angle DBC , or CBD . X. When a straight line standing on another straight line , makes the adjacent angles equal to one ...
... contained by AB , DB , is named the angle ABD , or DBA ; and that which is contained by DB , CB , is called the angle DBC , or CBD . X. When a straight line standing on another straight line , makes the adjacent angles equal to one ...
Σελίδα 3
... contained by a diameter and the part of the circumference cut off by the diameter . XIX . The center of a semicircle is the same with that of the circle . XX . Rectilineal figures are those which are contained by straight lines . XXI ...
... contained by a diameter and the part of the circumference cut off by the diameter . XIX . The center of a semicircle is the same with that of the circle . XX . Rectilineal figures are those which are contained by straight lines . XXI ...
Σελίδα 8
... contained by those sides equal to each other ; they shall likewise have their bases or third sides equal , and the two triangles shall be equal , and their other angles shall be equal , each to each , viz . those to which the equal ...
... contained by those sides equal to each other ; they shall likewise have their bases or third sides equal , and the two triangles shall be equal , and their other angles shall be equal , each to each , viz . those to which the equal ...
Σελίδα 22
... contained by the two sides of one of them greater than the angle contained by the two sides equal to them , of the other ; the base of that which has the greater angle , shall be greater than the base of the other . Let ABC , DEF be two ...
... contained by the two sides of one of them greater than the angle contained by the two sides equal to them , of the other ; the base of that which has the greater angle , shall be greater than the base of the other . Let ABC , DEF be two ...
Σελίδα 23
... contained by the sides of the one which has the greater base , shall be greater than the angle contained by the sides , equal to them , of the other . Let ABC , DEF be two triangles which have the two sides AB , AC , equal to the two ...
... contained by the sides of the one which has the greater base , shall be greater than the angle contained by the sides , equal to them , of the other . Let ABC , DEF be two triangles which have the two sides AB , AC , equal to the two ...
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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.