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

### Inni boken

Side 3

A

A

**semicircle**is the figure contained by a diameter and the part of the circumference cut off by the diameter . XIX . “ A segment of a circle is the figure contained by a straight line , and the circumference it cuts off . ” XX . Side 62

... at the distance GB , or GF , describe the

... at the distance GB , or GF , describe the

**semicircle**BHF , and produce DE to H : the square described upon EH shall be equal to the given rectilineal figure A. H B Join GH ; and because the straight line BF is 62 EUCLID'S ELEMENTS . Side 80

“ And this is all that is to be understood , when , in the Greek text and translations from it , the angle of the

“ And this is all that is to be understood , when , in the Greek text and translations from it , the angle of the

**semicircle**is said to be greater than any acute rectilineal angle , and the remaining angle less than any rectilineal ... Side 84

F B В с First , let the segment BAED be greater than a

F B В с First , let the segment BAED be greater than a

**semicircle**. Take ( III . 1. ) F the centre of the circle ABCD , and join BF , FD . And because the angle BFD is at the centre , and the angle BAD at the circumference , and that ... Side 85

For the same reason , because CBED is greater than a

For the same reason , because CBED is greater than a

**semicircle**, 2 . The angles CAD , CED , are equal : therefore ( Ax . 2. ) 3 . The whole angle BAD is equal to the whole angle BED . Wherefore the angles in the same segment , & c .### Hva folk mener - Skriv en omtale

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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 demonstrated describe diameter distance divided double draw equal angles exterior angle extremity fall figure four given circle given point given straight line given triangle gnomon 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...