## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added Elements of Plane and Spherical Trigonometry |

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Resultat 1-5 av 5

Side 28

To bisect a given finite

AB be the given

Describe ( 1. 1. ) upon it an equilateral triangle ABC , and bisect ( 9. 1. ) the angle

ACB ...

To bisect a given finite

**straight line**, that is , to divide it into two equal parts . LetAB be the given

**straight line**; it is required to divide it into two equal parts .Describe ( 1. 1. ) upon it an equilateral triangle ABC , and bisect ( 9. 1. ) the angle

ACB ...

Side 30

If , at a point in a

it , make the adjacent angles together equal to two right angles , these two

If , at a point in a

**straight line**, two other**straight lines**, upon the opposite sides ofit , make the adjacent angles together equal to two right angles , these two

**straight lines**are in one and the same**straight line**. At the point B in the**straight****line**... Side 41

Again , because the

angle GHF is equal - ( 29. 1.y to the angle GKD ; and it was shewn that the angle

AGK is equal to the angle GHF ; therefore also AGK is equal to GKD ; and they ...

Again , because the

**straight line**GK cuts the parallel**straight lines**EF , CD , theangle GHF is equal - ( 29. 1.y to the angle GKD ; and it was shewn that the angle

AGK is equal to the angle GHF ; therefore also AGK is equal to GKD ; and they ...

Side 183

Now AG is any

is at right angles to the plane itself ( def . 1 . 2. Sup . ) . AB is therefore at right ...

Now AG is any

**straight line**drawn in the plane of the lines AD , AF ; and when a**straight line**is at right angles to any**straight line**which it meets with in a plane , itis at right angles to the plane itself ( def . 1 . 2. Sup . ) . AB is therefore at right ...

Side 292

To supply the defects of his definition , he has therefore introduced the Axiom ,

that two

his definition of a

manner ...

To supply the defects of his definition , he has therefore introduced the Axiom ,

that two

**straight lines**cannot inclose a space ; on which Axiom it is , and not onhis definition of a

**straight line**, that his demonstrations are founded . As thismanner ...

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Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1819 |

Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1824 |

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common contained cosine cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular Euclid exterior extremity fall fore four fourth given given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism produced proportionals proposition proved Q. E. D. PROP radius ratio reason rectangle contained rectilineal figure right angles segment shewn sides similar sine solid square straight line taken tangent THEOR thing third touches triangle ABC wherefore whole

### Populære avsnitt

Side 56 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Side 19 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Side 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.

Side 62 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...

Side 62 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...

Side 130 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Side 76 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...

Side 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.

Side 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.

Side 55 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.