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

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Resultat 1-5 av 23

Side 1

The

between its extreme points . V. A superficies is that which has only length and

breadth . VI . The

that ...

The

**extremities**of a line are points . IV . A straight line is that which lies evenlybetween its extreme points . V. A superficies is that which has only length and

breadth . VI . The

**extremities**of a superficies are lines . VII . A plane superficies isthat ...

Side 2

An obtuse angle is that which is greater than a right angle . XII . An acute angle is

that which is less than a right angle . XIII . “ A term or boundary is the

any thing . " XIV . A figure is that which is inclosed by 2 EUCLID'S ELEMENTS .

An obtuse angle is that which is greater than a right angle . XII . An acute angle is

that which is less than a right angle . XIII . “ A term or boundary is the

**extremity**ofany thing . " XIV . A figure is that which is inclosed by 2 EUCLID'S ELEMENTS .

Side 11

Upon the same base , and on the same side of it , there cannot be two triangles

that have their sides which are terminated in one

one another , and likewise those which are terminated in the other

be ...

Upon the same base , and on the same side of it , there cannot be two triangles

that have their sides which are terminated in one

**extremity**of the base equal toone another , and likewise those which are terminated in the other

**extremity**. If itbe ...

Side 12

terminated in the

sides CB , DB , that are terminated in B. E c Α . B B Join CD . Then , in the case in

which the vertex of each of the triangles is without the other triangle , because ...

terminated in the

**extremity**A of the base equal to one another , and likewise theirsides CB , DB , that are terminated in B. E c Α . B B Join CD . Then , in the case in

which the vertex of each of the triangles is without the other triangle , because ...

Side 13

... then , upon the same base EF , and upon the same side of it , there can two

triangles that have their sides wbich are terminated in one

equal to one another , and likewise their sides terminated in the other

... then , upon the same base EF , and upon the same side of it , there can two

triangles that have their sides wbich are terminated in one

**extremity**of the baseequal to one another , and likewise their sides terminated in the other

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The Synoptical Euclid; Being the First Four Books of Euclid's Elements of ... Uten tilgangsbegrensning - 1854 |

### Vanlige uttrykk og setninger

ABCD AC is equal AF is equal angle ABC angle ACB angle BAC angle BCD angle equal base base BC bisected centre circle ABC circumference coincide common cuts the circle demonstrated describe diameter distance divided double draw equal angles 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 PROBLEM produced Q.E.D. PROP reason rectangle contained rectilineal figure remaining angle required to describe right angles segment semicircle shown sides square of AC straight line AC THEOREM 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...