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

### Inni boken

Resultat 1-5 av 14

Side 3

A diameter of a

both ways by the circumference . XVIII . A semicircle is the figure contained by a

diameter and the part of the circumference

A diameter of a

**circle**is a straight line drawn through the centre , and terminatedboth ways by the circumference . XVIII . A semicircle is the figure contained by a

diameter and the part of the circumference

**cut**off by the diameter . XIX . Side 65

A segment of a

circumference it

by the straight line and the circumference . ” VIII . An angle in a segment is the

angle ...

A segment of a

**circle**is the figure contained by a straight line and thecircumference it

**cuts**off . VII . “ The angle of a segment is that which is containedby the straight line and the circumference . ” VIII . An angle in a segment is the

angle ...

Side 67

AB falls within the

THEOREM . If a straight line drawn through the centre of a

line in it which does not pass through the centre , it shall

AB falls within the

**circle**. Wherefore , if any two points , & c . , Q.E.D. PROP . III . -THEOREM . If a straight line drawn through the centre of a

**circle**bisect a straightline in it which does not pass through the centre , it shall

**cut**it at right angles ... Side 68

E the centre of the

... If in a

the centre , they do not bisect each other . Let ABCD be a

two ...

E the centre of the

**circle**, and join EA , EB . Then , because AF is equal ( Hyp . )... If in a

**circle**two straight lines**cut**one another which do not both pass throughthe centre , they do not bisect each other . Let ABCD be a

**circle**, and AC , BD ,two ...

Side 86

Upon the same straight line , and upon the same side of it , there cannot be two

similar segments of circles , not ... D A Then , because the circle ACB

III .

Upon the same straight line , and upon the same side of it , there cannot be two

similar segments of circles , not ... D A Then , because the circle ACB

**cuts the****circle**ADB in the two points A , B , they cannot cut one another in any other point (III .

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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...