## 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 ... |

### From inside the book

Page xxvii

To determine the position of

To determine the position of

**a**point , at which lines drawn from three given points shall make with each other angles equal to given angles . 6. To divide**a straight line into two parts such**that the**rectangle contained**by them may be ... Page xxviii

**contained**by the**whole**and**one**of the**parts**may be equal**to**the square of**a**given**line**, which is less than the**line to**be divided . 10.**To**divide**a**given**line into two such parts**, that the**rectangle contained**by the**whole line**... Page xxix

From the bisection of

From the bisection of

**a**given arc of**a**circle ,**to**draw**a straight line such**that the**part**of it intercepted**between**...**so**that the**rectangle contained**by the perpendiculars let fall upon it from the other**two**, may be equal**to a**given ... Page xli

The

The

**rectangle contained**by the segments of the base adjacent**to**the angles is equal**to**the square of either line drawn from the vertex ...**A**given**straight line**being divided**into**any three**parts**;**to**determine**a**point**such**, that lines ... Page xlv

**a**15. If from the extremities of any chord**in a**circle**straight lines**be drawn**to**any point**in**the circumference ... any line be drawn**to**the former , and cutting the circumference ; the**rectangle contained**by this line and the**part**of ...### What people are saying - Write a review

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### Other editions - View all

### Common terms and phrases

ABCD base centre chord circle circle ABC circumference common contained determine diameter difference distance divided double draw draw any line equal equiangular Eucl extremities figure given angle given circle given in position given line given point given ratio greater half intercepted Join AE less Let ABC let fall line given line joining line required lines be drawn lines drawn manner mean proportional meet opposite sides parallel to BC parallelogram passes pendicular perpendicular point of contact point of intersection points of bisection produced radius rectangle right angles segments semicircle shewn similar squares straight line tangent trapezium triangle ABC whence

### Popular passages

Page 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.

Page 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.

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

Page 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.

Page 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...

Page 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.

Page 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.

Page 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.

Page 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.

Page 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.