A Supplement to the Elements of EuclidG. and W. B. Whittaker, 1819 - 410 sider |
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Side 108
... chord which shall be bisected in that point . Let A be a given point within the circle BCD : It is required to draw , through A , a chord of the circle BCD , which shall be bisected in the point A. Find ( E. 1. 3. ) the centre K of the ...
... chord which shall be bisected in that point . Let A be a given point within the circle BCD : It is required to draw , through A , a chord of the circle BCD , which shall be bisected in the point A. Find ( E. 1. 3. ) the centre K of the ...
Side 110
... chords of a circle which cut a diameter in the same point and at equal angles , are equal to one another . Let any two chords AB , CD of the circle ADBC E A G M L D B K F cut a diameter EF in the same point G , and make with it the AGE ...
... chords of a circle which cut a diameter in the same point and at equal angles , are equal to one another . Let any two chords AB , CD of the circle ADBC E A G M L D B K F cut a diameter EF in the same point G , and make with it the AGE ...
Side 111
... chords , making with one another an angle equal to a given rectili- neal angle . Let G be a given point in the circle ADBC , A Ꮓ X D B K Y H and XHY a given rectilineal angle : It is required to draw through G two equal chords of the ...
... chords , making with one another an angle equal to a given rectili- neal angle . Let G be a given point in the circle ADBC , A Ꮓ X D B K Y H and XHY a given rectilineal angle : It is required to draw through G two equal chords of the ...
Side 112
... chord AB = chord CD . PROP . VI . 7. THEOREM . If the diameters of two circles are in the same straight line , and have a common ex- tremity , the two circles shall touch one another . For since ( hyp . ) the two diameters are in the ...
... chord AB = chord CD . PROP . VI . 7. THEOREM . If the diameters of two circles are in the same straight line , and have a common ex- tremity , the two circles shall touch one another . For since ( hyp . ) the two diameters are in the ...
Side 138
... chord , the angle which the one makes with any perpendicular to the chord , shall be equal to the angle which the other makes with the diameter of the circle that passes through the given point . Let C be a given point in the ...
... chord , the angle which the one makes with any perpendicular to the chord , shall be equal to the angle which the other makes with the diameter of the circle that passes through the given point . Let C be a given point in the ...
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Vanlige uttrykk og setninger
ABCD bisect centre chord circle ABC circle described circumference constr decagon describe a circle describe the circle diameter distance divided double draw a straight draw E equi equiangular equilateral and equiangular EUCLID Euclid's Elements F draw find a point finite straight line given circle given finite straight given point given ratio given square given straight line half hypotenuse inscribed isosceles join K less Let ABC lines be drawn manifest manner meet the circumference number of equal number of sides parallel to BC parallelogram pass perimeter point G polygon PROBLEM produced PROP rectangle contained rectilineal figure remaining sides required to describe required to draw rhombus right angles segment semi-diameter straight line cutting straight line joining tangent THEOREM three given touch the circle trapezium vertex
Populære avsnitt
Side 278 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Side 326 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the...
Side 76 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 2 - ... angles equal; and conversely if two angles of a triangle are equal, two of the sides are equal. 3. If two triangles have the three sides of one equal to the three sides of the other, each to each, do you think the two triangles are alike in every respect ? 4. If two triangles have the three angles of one equal to the three angles of the other, each to each, do you think the two triangles are necessarily alike in every respect ? 5. Draw two triangles, the angles of one being equal to the angles...
Side 309 - Divide a straight line into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square on the other part.
Side 256 - ... line and the extremities of the base have the same ratio which the other sides of the triangle have to one...
Side 175 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...
Side 327 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Side 86 - In every triangle, the square of the side subtending any 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. Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular...
Side 5 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC. In BC take any point D, and join AD; and at the point A, in the straight line AD, make (I.