## 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

... two lines such that the sum of their squares may be equal to

... two lines such that the sum of their squares may be equal to

**a**given square , and their**rectangle**equal to**a**given**rectangle**. 9. To divide**a straight line into two parts**,**so**that the**rectangle contained**by the**whole**and**one**of the**parts**... Page xxviii

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**parts**, that the**rectangle contained**by the**whole line**, and**one**of the**parts**may be ( m ) times the square of the other**part**; ( m ) being**whole**or fractional . 1.1 .**To**divide**a**given**line into two such parts**, that the square of the**one**... Page xxix

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**between**the**segments**of the side . 30. From the common extremity of the diameters of**two**semi- circles , given**in**magnitude and position ;**to**draw**a line**meeting the circumferences**so**that the**rectangle contained**by the**two**chords CONTENTS ... Page xli

**To**which is Added**an**Appendix**Containing**the**Elements**of Plane Trigonometry ... Miles Bland. COR .**1**. The**rectangle contained**by the**segments**of the base adjacent**to**the angles is equal**to**the square of either**line**...**whole line**thus ... Page xlv

**To**which is Added**an**Appendix**Containing**the**Elements**of Plane Trigonometry ... Miles Bland. 15. If from the extremities of any chord**in a**circle**straight lines**be drawn**to**any point**in**the circumference meeting**a**diameter per- pendicular ...### Contents

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### Common terms and phrases

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

### 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.