## A Supplement to the Elements of Euclid |

### From inside the book

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Page 118

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**given**straight line L. Q. E. F. PROP . XI . 13. PROBLEM . To describe a**circle**, the circum- ference of which shall pass through a**given**point , and touch a**given**straight line in another**given**point . Let B be a**given**point in the**given**... Page 119

... circle , the circum- ference of which shall pass through a given point , and touch a

... circle , the circum- ference of which shall pass through a given point , and touch a

**given circle**in another given point ; the two points not lying in a tangent to the circle . Let B be a given point in the circle AB , and C K B E C any ... Page 120

... given point , and also touch a

... given point , and also touch a

**given circle**. Let AB be a**given circle**, and let C be a given E F X K B point in the given straight line XY : It is required to describe a circle which shall touch XY in C , and which shall also touch the ... Page 121

... circle AB in B. 16. COR . It is manifest that , in the same man- ner , a circle may be described which shall touch a

... circle AB in B. 16. COR . It is manifest that , in the same man- ner , a circle may be described which shall touch a

**given circle**in a given point , and which shall , also , touch another**given circle**. For , if a straight line be drawn ... Page 122

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**given**semi - diameter of the other ; from B , as a centre , at the distance BA describe the**circle**AF ; from AB , produced , if necessary , cut off ( E. 3. 1. ) AD AC ; through D draw ( E. 31. 1. ) DZ parallel to XY ; from B as a centre ...### Other editions - View all

### Common terms and phrases

ABCD bisect centre chord circle ABC circle described circumference constr decagon describe a circle describe the circle diameter distance divided double draw a straight draw E equi equiangular equilateral and equiangular EUCLID Euclid's Elements F draw find a point finite straight line given circle given finite straight given point given ratio given square given straight line half hypotenuse inscribed isosceles join K less Let ABC lines be drawn manifest manner meet the circumference number of equal number of sides parallel to BC parallelogram pass perimeter point G polygon PROBLEM produced PROP rectangle contained rectilineal figure remaining sides required to describe required to draw rhombus right angles segment semi-diameter straight line cutting straight line joining tangent THEOREM three given touch the circle trapezium vertex

### Popular passages

Page 278 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.

Page 326 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the...

Page 76 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.

Page 2 - ... angles equal; and conversely if two angles of a triangle are equal, two of the sides are equal. 3. If two triangles have the three sides of one equal to the three sides of the other, each to each, do you think the two triangles are alike in every respect ? 4. If two triangles have the three angles of one equal to the three angles of the other, each to each, do you think the two triangles are necessarily alike in every respect ? 5. Draw two triangles, the angles of one being equal to the angles...

Page 309 - Divide a straight line into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square on the other part.

Page 256 - ... line and the extremities of the base have the same ratio which the other sides of the triangle have to one...

Page 175 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...

Page 327 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.

Page 86 - In every triangle, the square of the side subtending any of the acute angles is less than the squares of the sides containing that angle by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Let ABC be any triangle, and the angle at B one of its acute angles, and upon BC, one of the sides containing it, let fall the perpendicular...

Page 5 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC. In BC take any point D, and join AD; and at the point A, in the straight line AD, make (I.