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

### Inni boken

Side 2

An acute angle is that which is

An acute angle is that which is

**less**than a right angle . XIII . " A term or boundary is the extremity of any thing . " XIV . A figure is that which is inclosed by 2 EUCLID'S ELEMENTS . Side 6

If a straight line meet two straight lines , so as to make the two interior angles on the same side of it taken together

If a straight line meet two straight lines , so as to make the two interior angles on the same side of it taken together

**less**than two right angles , these straight lines being continually produced , shall at length meet upon that side ... Side 8

From the greater of two given straight lines to cut off a part equal to the

From the greater of two given straight lines to cut off a part equal to the

**less**. . Let AB and C be the two given straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part equal to C ... Side 11

DB equal to AC , the

DB equal to AC , the

**less**, and join DC . Therefore because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , 1. The two sides DB , BC , are equal to the two AC , CB , each to each ... Side 15

The angle DBE is equal to the angle CBE , the

The angle DBE is equal to the angle CBE , the

**less**to the greater , which is impossible ; therefore 4. Two straight lines cannot have a common segment . PROP . XII . - PROBLEM . To draw a BOOK I. - PROP . XI . 15.### 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...