## The synoptical Euclid; being the first four books of Euclid's Elements of geometry, with exercises, by S.A. Good |

### Inni boken

Side 7

the straight lines CA , CB , to the points A , B ;

the straight lines CA , CB , to the points A , B ;

**ABC**shall be an equilateral**triangle**. Because the point A is the centre of the circle BCD , ( Definition 15. ) 1. AC is equal to AB ; and because the point B is the centre of the ... Side 9

Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz . ... and the

Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz . ... and the

**triangle ABC**to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be ... Side 10

The angles at the base of an isosceles

The angles at the base of an isosceles

**triangle**are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal . Let**ABC**' be an isosceles**triangle**, of which the side AB is ... Side 11

which are the angles at the base of the

which are the angles at the base of the

**triangle ABC**. And it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . Therefore the angles at the base , & c . Side 12

Then , in the case in which the vertex of each of the

Then , in the case in which the vertex of each of the

**triangles**is without the other**triangle**, because AC is equal to AD , ( I. 5. ) 1. The angle ACD is equal to the ... Let**ABC**, DEF , be two**triangles**having the 12 EUCLID'S ELEMENTS .### Hva folk mener - Skriv en omtale

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### Vanlige uttrykk og setninger

ABCD AC is equal AF is equal angle ABC angle ACB angle BAC angle BCD angle equal base BC bisected centre circle ABC circumference coincide common demonstrated describe diameter distance divided double draw equal angles equal Constr exterior angle extremity fall figure four given circle given point given straight line given triangle greater impossible inscribed join less Let ABC likewise manner meet opposite angles parallel parallelogram pass pentagon perpendicular point F produced Q.E.D. PROP reason rectangle contained rectilineal figure remaining angle required to describe right angles segment semicircle shown side BC sides square of AC straight line AC touches the circle triangle ABC twice the rectangle wherefore whole

### Populære avsnitt

Side 26 - If two triangles have two angles of the one equal to two angles of the other, each to each ; and one side equal to one side, viz. either the sides adjacent to the equal...

Side 22 - If from the ends of a side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle.

Side 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 1 - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. vm. "A plane angle is the inclination of two lines to one another in a plane, which meet together, but are not in the same direction.

Side 97 - 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 7 - AB; but things which are equal to the same are equal to one another...

Side 14 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.

Side 53 - IF a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part.

Side 41 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.

Side 52 - 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...