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 14
... right angles to a given straight line , from a given point in the same . Let AB be the given straight line , and Ca given point in it . It is required to draw a straight line from the point C at right angles to AB D C E B In AC take any ...
... right angles to a given straight line , from a given point in the same . Let AB be the given straight line , and Ca given point in it . It is required to draw a straight line from the point C at right angles to AB D C E B In AC take any ...
Side 15
... angles equal to one another , each of them is a right angle , and the straight line which stands upon the other is ... angles which one straight line makes with another upon one side of it , are either two right angles , or are together ...
... angles equal to one another , each of them is a right angle , and the straight line which stands upon the other is ... angles which one straight line makes with another upon one side of it , are either two right angles , or are together ...
Side 16
... angles CBA , ABE , add the angle EBD to each of these equals ; therefore the angles CBE , EBD are equal to the three ... right angles ; therefore the angles DBA , ABC are together equal to two right angles . ( L. 1. ) Wherefore , when a ...
... angles CBA , ABE , add the angle EBD to each of these equals ; therefore the angles CBE , EBD are equal to the three ... right angles ; therefore the angles DBA , ABC are together equal to two right angles . ( L. 1. ) Wherefore , when a ...
Side 17
... angles ' shall be equal . Let the two straight lines AB , CD cut one another in the point E. Then the angle AEC ... right angles . ( 1. 13. ) Again , because the straight line DE makes with AB at the point E , the adjacent angles AED ...
... angles ' shall be equal . Let the two straight lines AB , CD cut one another in the point E. Then the angle AEC ... right angles . ( 1. 13. ) Again , because the straight line DE makes with AB at the point E , the adjacent angles AED ...
Side 18
... 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 exterior angle of ...
... 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 exterior angle of ...
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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.