## 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 |

### Inni boken

Resultat 1-5 av 5

Side 54

Let A and BC be two straight lines ; and let BC be divided into any parts in the

points D , E ; the rectangle A.BC is equal to the several rectangles A.BD , A.DE , A

.EC. From the point B

...

Let A and BC be two straight lines ; and let BC be divided into any parts in the

points D , E ; the rectangle A.BC is equal to the several rectangles A.BD , A.DE , A

.EC. From the point B

**draw**( 11. 1. ) BF at right angles to BC , and make BG equal...

Side 78

from D

angle , and the angle DAH less than a right angle , the side DH of the triangle

DAH is less than the side DA ( 19. 1. ) . The point H , therefore , is within the H Н ...

from D

**draw**DH at right angles to AG ; E and because the angle DHA is a right Gangle , and the angle DAH less than a right angle , the side DH of the triangle

DAH is less than the side DA ( 19. 1. ) . The point H , therefore , is within the H Н ...

Side 98

To describe a square about a given circle . Let ABCD be the given circle ; it is

required to describe a square about it .

ABCD , at right angles to one another , and through the points A , B , C , D

17.

To describe a square about a given circle . Let ABCD be the given circle ; it is

required to describe a square about it .

**Draw**two diameters AC , BD of the circleABCD , at right angles to one another , and through the points A , B , C , D

**draw**(17.

Side 186

In the plane

perpendicular to BC . If then AD be also perpendicular to the plane BH , the thing

required is already done ; but if it be not , from the point D

In the plane

**draw**any straight line BC , and from the point A**draw**( 12. 1. ) ADperpendicular to BC . If then AD be also perpendicular to the plane BH , the thing

required is already done ; but if it be not , from the point D

**draw**( 11. 1. ) , in the ... Side 216

Let ADB be a semicircle , of which the centre is C , and let CD be at right angles

to AB ; let DB and DA be squares described on DC ,

thus constructed revolve about DC : then , the sector BCD , which is the half of the

...

Let ADB be a semicircle , of which the centre is C , and let CD be at right angles

to AB ; let DB and DA be squares described on DC ,

**draw**CE , and let the figurethus constructed revolve about DC : then , the sector BCD , which is the half of the

...

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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.