## 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 227

The sum of the sines of any two arches of a circle , is to the

sines , as the tangent of half the sum of the arches to the tangent of half their

AEG ...

The sum of the sines of any two arches of a circle , is to the

**difference**of theirsines , as the tangent of half the sum of the arches to the tangent of half their

**difference**. Let AB , AC be two arches of a circle ABCD ; let E be the centre , andAEG ...

Side 229

Again , the exterior angle ACB is equal to the two interior CAD , ADC , and

therefore CAD is the

for ABC is equal to ADC . Wherefore also DBF , which is the half of CAD , or BFG ,

which ...

Again , the exterior angle ACB is equal to the two interior CAD , ADC , and

therefore CAD is the

**difference**of the angles ACB , ADC , that is of ACB , ABC ,for ABC is equal to ADC . Wherefore also DBF , which is the half of CAD , or BFG ,

which ...

Side 230

the sum of the segments of the base is to the sum of the sides as the

the sides to the

triangle , twice the rectangle contained by any two sides is to the

the sum of the segments of the base is to the sum of the sides as the

**difference**ofthe sides to the

**difference**of the segments of the base . Q. E. D. PROP . VI . In anytriangle , twice the rectangle contained by any two sides is to the

**difference**... Side 233

If there be two unequal magnitudes , half their

is equal to the greater ; and half their

to the less . Let AB and BC be two unequal magnitudes , of which AB is the ...

If there be two unequal magnitudes , half their

**difference**added to half their sumis equal to the greater ; and half their

**difference**taken from half their sum is equalto the less . Let AB and BC be two unequal magnitudes , of which AB is the ...

Side 267

The sum of the tangents of any two arches , is to the

as the sine of the sum of the arches , to the sine of their

B sin ( A + B ) that is , because Let A and B be two arches , tan A + tan B : tan A ...

The sum of the tangents of any two arches , is to the

**difference**of their tangents ,as the sine of the sum of the arches , to the sine of their

**difference**. + COS A cosB sin ( A + B ) that is , because Let A and B be two arches , tan A + tan B : tan A ...

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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.