The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth BooksMacmillan, 1886 - 400 Seiten |
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... circumference . ] 18. A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter . 19. A segment of a circle is the figure contained by a straight line and the circumference which it ...
... circumference . ] 18. A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter . 19. A segment of a circle is the figure contained by a straight line and the circumference which it ...
Seite 72
... circumference it cuts off . 7. The angle of a segment is that which is contained by the straight line and the circumference . 8. An angle in a segment is the angle contained by two straight lines drawn from any point in the ...
... circumference it cuts off . 7. The angle of a segment is that which is contained by the straight line and the circumference . 8. An angle in a segment is the angle contained by two straight lines drawn from any point in the ...
Seite 74
... circumference of a circle , the straight line which joins them shall fall within the circle . Let ABC be a circle , and A and B any two points in the circumference : the straight line drawn from A to B shall fall within the circle . For ...
... circumference of a circle , the straight line which joins them shall fall within the circle . Let ABC be a circle , and A and B any two points in the circumference : the straight line drawn from A to B shall fall within the circle . For ...
Seite 78
... circumference , the greatest is that in which the centre is , and the other part of the diameter is the least ; and , of any others , that which is nearer to the straight line which passes through the centre , is always greater than one ...
... circumference , the greatest is that in which the centre is , and the other part of the diameter is the least ; and , of any others , that which is nearer to the straight line which passes through the centre , is always greater than one ...
Seite 79
... circumference ; and FB is greater than FC , and FC than FG . Also , there can be drawn two equal straight lines from the point F to the circumference , one on each side of the shortest line FD . For , at the point E , in the straight ...
... circumference ; and FB is greater than FC , and FC than FG . Also , there can be drawn two equal straight lines from the point F to the circumference , one on each side of the shortest line FD . For , at the point E , in the straight ...
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ABCD angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC BC is equal bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore