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 páginas |
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Página 11
... THEOREM . Upon the same base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one extremity of the base , equal to one another , and likewise those which are terminated in the ...
... THEOREM . Upon the same base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one extremity of the base , equal to one another , and likewise those which are terminated in the ...
Página 16
... THEOREM . If at a point in a straight line , two other straight lines , upon the opposite sides of is , make the adjacent angles together equal to two right angles ; then these two straight lines shall be in one and the same straight ...
... THEOREM . If at a point in a straight line , two other straight lines , upon the opposite sides of is , make the adjacent angles together equal to two right angles ; then these two straight lines shall be in one and the same straight ...
Página 17
... THEOREM . If two straight lines cut one another , the vertical , or opposite angles ' shall be equal . Let the two straight lines AB , CD cut one another in the point E. Then the angle AEC shall be equal to the angle DEB , and the angle ...
... THEOREM . If two straight lines cut one another , the vertical , or opposite angles ' shall be equal . Let the two straight lines AB , CD cut one another in the point E. Then the angle AEC shall be equal to the angle DEB , and the angle ...
Página 18
... THEOREM . Any two angles of a triangle are together less than two right angles . Let ABC be any triangle . Then any two of its angles together shall be less than two right angles . B C D Produce any side BC to D. Then because ACD is the ...
... THEOREM . Any two angles of a triangle are together less than two right angles . Let ABC be any triangle . Then any two of its angles together shall be less than two right angles . B C D Produce any side BC to D. Then because ACD is the ...
Página 19
... THEOREM . The greater angle of every triangle is subtended by the greater side , or , has the greater side opposite to it . Let ABC be a triangle of which the angle ABC is greater than the angle BCA . Then the side AC shall be greater ...
... THEOREM . The greater angle of every triangle is subtended by the greater side , or , has the greater side opposite to it . Let ABC be a triangle of which the angle ABC is greater than the angle BCA . Then the side AC shall be greater ...
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Términos y frases comunes
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
Pasajes populares
Página 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...
Página 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.
Página 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.
Página 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.
Página 26 - ... upon the same side together equal to two right angles, the two straight lines shall be parallel to one another.
Página 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.
Página 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.
Página 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...
Página 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.
Página 67 - A proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate or capable of innumerable solutions.