## Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement ... to which are Added, Elements of Plane and Sphericale Trigonometry ... From the Last London Ed., Enl |

### From inside the book

Results 1-5 of 68

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**given**, from which the properties of proportionals can be deduced by reasonings , which , at the same time that they ...**straight line**. A new axiom is also introduced in the room of the 12th , for the purpose of demonstrating more easily ... Page 12

... a given finite straight line . Let AB be the

... a given finite straight line . Let AB be the

**given straight line**; it is required to describe an equi . lateral triangle upon it . From the centre A , at the dis- tance AB , describe ( 3. Postulate ) the circle BCD , and from the cen ... Page 13

... straight line AL is equal to BC . Wherefore , from the given point A , a straight line AL has been drawn equal to the

... straight line AL is equal to BC . Wherefore , from the given point A , a straight line AL has been drawn equal to the

**given straight line**BC . PROP . III . PROB . From the greater of two**given straight lines**to cut of a part equal to ... Page 17

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**given**rectilineal angle , that is , to divide it into two equal angles A Let ...**straight line**AF bisects the angle BAC . Because AD is equal to AE , and AF ...**given**rectilineal angle BAC is bisect- ad by the**straight line**AF . SCHOLIUM ... Page 18

... straight line at right angles to a

... straight line at right angles to a

**given straight line**, from a given point in that line . Let AB be a**given straight line**, and C a point given in it ; it is requi red to draw a straight line from the point C at right angles to AB F ...### Other editions - View all

### Common terms and phrases

ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore