## 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 sider |

### Fra bogen

Resultater 1-5 af 19

Side xix

... ratio . 24. If the base of a triangle be produced so that the whole may be to the part produced in the

... 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 ... Side xli

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**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 ... Side 47

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**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 . Side 48

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**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 ... Side 66

... ratio , take AB and EF in that ratio , and make the same construction as in the proposition . ( 67. ) To determine a ...

... 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 ...### Indhold

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### Andre udgaver - Se alle

### Almindelige termer og sætninger

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

### Populære passager

Side 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.

Side 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.

Side 230 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.

Side 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.

Side 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...

Side 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.

Side 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.

Side 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.

Side 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.

Side 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.