Geometrical Problems Deducible from the First Six Books of Euclid, Arranged and Solved: To which is Added an Appendix Containing the Elements of Plane Trigonometry ...J. Smith, 1819 - 377 σελίδες |
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Αποτελέσματα 1 - 5 από τα 100.
Σελίδα 1
... ( Eucl . i . 32. ) and consequently less than ACD . But the greater angle is subtended by the greater side ( Eucl . i . 19. ) ; therefore AD is greater than AC . In the same manner every other line drawn from A to BD may be shewn to be ...
... ( Eucl . i . 32. ) and consequently less than ACD . But the greater angle is subtended by the greater side ( Eucl . i . 19. ) ; therefore AD is greater than AC . In the same manner every other line drawn from A to BD may be shewn to be ...
Σελίδα 2
... ( Eucl . i . 20. ) ; therefore , & c . ( 3. ) Through a given point to draw a straight line which shall make equal angles with two straight lines given in position . Let P be the given point , and BE , CF the lines given in position ...
... ( Eucl . i . 20. ) ; therefore , & c . ( 3. ) Through a given point to draw a straight line which shall make equal angles with two straight lines given in position . Let P be the given point , and BE , CF the lines given in position ...
Σελίδα 4
... ( Eucl . i . 20. ) BC is less than Bp , PC , and therefore AP , PB are less than Ap , PB ; therefore , & c . ( 7. ) Of all straight lines which can be drawn from a given point to an indefinite straight line , that which is nearer to the ...
... ( Eucl . i . 20. ) BC is less than Bp , PC , and therefore AP , PB are less than Ap , PB ; therefore , & c . ( 7. ) Of all straight lines which can be drawn from a given point to an indefinite straight line , that which is nearer to the ...
Σελίδα 5
... ( Eucl . i . 16. ) , and therefore greater than AGF , hence ( Eucl . i . 19. ) AG is greater than AF . In the same manner it may be shewn that AH is greater than AG . on each side Then AE = = And from A there can only be drawn to BC two ...
... ( Eucl . i . 16. ) , and therefore greater than AGF , hence ( Eucl . i . 19. ) AG is greater than AF . In the same manner it may be shewn that AH is greater than AG . on each side Then AE = = And from A there can only be drawn to BC two ...
Σελίδα 6
... ( Eucl . vi . 2. ) EP : PF :: ED : DA , i . e . in a ratio of equality . COR . If it be required to draw a line through P which shall be terminated by the given lines , and divided in any given ratio in P , draw PD parallel to AC and take ...
... ( Eucl . vi . 2. ) EP : PF :: ED : DA , i . e . in a ratio of equality . COR . If it be required to draw a line through P which shall be terminated by the given lines , and divided in any given ratio in P , draw PD parallel to AC and take ...
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD angle ABC base bisects the angle centre chord circle ABC circles cut circles touch circumference describe a circle divided draw any line drawn parallel duplicate ratio equal angles equiangular Eucl extremities given angle given circle given in position given line given point given ratio given straight line given triangle inscribed intercepted isosceles triangle Join AE Join BD Let AB Let ABC let fall line given line joining line required lines be drawn lines drawn mean proportional opposite side parallel to BC parallelogram pendicular perpendicular be drawn point of bisection point of contact point of intersection quadrant radius rectangle contained right angles right-angled triangle segments semicircle shewn tangent touches the circle trapezium triangle ABC vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 124 - If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those sides produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight '.line which joint the points of section, shall be parallel to the remaining side of the triangle.
Σελίδα xiii - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle,. shall be equal to the square of the line which touches it.
Σελίδα 158 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other...
Σελίδα 160 - Upon a given straight line, to describe a segment of a circle, containing an angle equal to a given angle. Let AB be the given straight line, and C the given angle ; it is required to.
Σελίδα 230 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Σελίδα 157 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Σελίδα 33 - FC ; (ax. 1.) and FA, FB, FC are equal to one another : wherefore the circle described from the centre F, at the distance of one of them, will pass through the extremities of the other two, and be described about the triangle ABC.
Σελίδα xxv - ... the squares of the diagonals, is equal to the sum of the squares of the bisected sides together with four times the square of the line joining those points of bisection.
Σελίδα 248 - If an equilateral triangle be inscribed in a circle, and the adjacent arcs cut off by two of its sides be bisected, the line joining the points of bisection shall be trisected by the sides.
Σελίδα 355 - The sine of an angle is equal to the sine of its supplement. The sine rule Consider fig.