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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Σελίδα xix
... ratio . 24. If the base of a triangle be produced so that the whole may be to the part produced in the duplicate ratio of the sides ; the line joining the vertex , and the extremity of the part produced will be a mean proportional ...
... ratio . 24. If the base of a triangle be produced so that the whole may be to the part produced in the duplicate ratio of the sides ; the line joining the vertex , and the extremity of the part produced will be a mean proportional ...
Σελίδα xli
... duplicate ratio of the adjacent sides . 28. If one circle be circumscribed and another inscribed in a given triangle , and a line be drawn from the vertical angle to the centre of the inner , and produced to the circumference of the ...
... duplicate ratio of the adjacent sides . 28. If one circle be circumscribed and another inscribed in a given triangle , and a line be drawn from the vertical angle to the centre of the inner , and produced to the circumference of the ...
Σελίδα 47
... duplicate ratio of AB : AD . For the same reason , AG : AB in the duplicate ratio of AC : AB , .. AG : AH in the duplicate ratio of AC Sect . 2. ] 47 GEOMETRICAL PROBLEMS .
... duplicate ratio of AB : AD . For the same reason , AG : AB in the duplicate ratio of AC : AB , .. AG : AH in the duplicate ratio of AC Sect . 2. ] 47 GEOMETRICAL PROBLEMS .
Σελίδα 48
... duplicate ratio of AC : AD . In the same manner it may be shewn that AG AH in the duplicate ratio of AE : AF , .. ( Eucl . v . 15. ) the duplicate ratio of AC : AD , is the same with the duplicate ratio of AE : AF , and . AC AD :: AE ...
... duplicate ratio of AC : AD . In the same manner it may be shewn that AG AH in the duplicate ratio of AE : AF , .. ( Eucl . v . 15. ) the duplicate ratio of AC : AD , is the same with the duplicate ratio of AE : AF , and . AC AD :: AE ...
Σελίδα 66
... ratio , take AB and EF in that ratio , and make the same construction as in the proposition . ( 67. ) To determine a ... duplicate ratio of OC : OD , i . e . in the duplicate ratio of AO : OB . But ( Eucl . vi . 8. Cor . ) AE EB in the ...
... ratio , take AB and EF in that ratio , and make the same construction as in the proposition . ( 67. ) To determine a ... duplicate ratio of OC : OD , i . e . in the duplicate ratio of AO : OB . But ( Eucl . vi . 8. Cor . ) AE EB in the ...
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD angle ABC angles at F base centre chord circle ABC circles cut circles touch circumference describe a circle divided draw a line draw the diameter drawn parallel duplicate ratio equal angles equiangular Eucl extremities G draw given angle given circle given in position given line given point given ratio given square given straight line given triangle 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 point of bisection point of contact point of intersection point required radius rectangle right angles segments semicircle shewn tangent touching the circle trapezium triangle ABC
Δημοφιλή αποσπάσματα
Σελίδα 14 - IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section.
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 230 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Σελίδα 327 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
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 212 - 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 123 - If from a point, without a parallelogram, there be drawn two straight lines to the extremities of the two opposite sides, between which, when produced, the point does not lie, the difference of the triangles thus formed is equal to half the parallelogram. Ex. 2. The two triangles, formed by drawing straight lines from any point within a parallelogram to the extremities of its opposite sides, are together half of the parallelogram.
Σελίδα 305 - Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle.
Σελίδα 247 - The perpendicular from the vertex on the base of an equilateral triangle is equal to the side of an equilateral triangle inscribed in a circle, whose diameter is the base.
Σελίδα 299 - AB be equal to the given bisecting line ; and upon it describe a segment of a circle containing an angle equal to the given angle.