## Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement on the Quadrature of the Circle and the Geometry of Solids ... |

### Inni boken

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Side ix

The demonstration of the

Geometry ; that of the sixth is new , as far as I know ; as is also the solution of the

problem in the nineteenth proposition , --a problem which , though in itself ...

The demonstration of the

**fourth**proposition is from LEGENDRE's Elements ofGeometry ; that of the sixth is new , as far as I know ; as is also the solution of the

problem in the nineteenth proposition , --a problem which , though in itself ...

Side 108

V. If there be four magnitudes , and if any equimultiples whatsoever be taken of

the first and third , and any equimultiples whatsoever of the second and

and if , according as the multiple of the first is greater than the multiple of the ...

V. If there be four magnitudes , and if any equimultiples whatsoever be taken of

the first and third , and any equimultiples whatsoever of the second and

**fourth**,and if , according as the multiple of the first is greater than the multiple of the ...

Side 109

... greater than the multiple of the

second a greater ratio than the third magnitude has to the

contrary , the third is said to have to the

second .

... greater than the multiple of the

**fourth**; then the first is said to have to thesecond a greater ratio than the third magnitude has to the

**fourth**; and , on thecontrary , the third is said to have to the

**fourth**a less ratio than the first has to thesecond .

Side 110

If four magnitudes are continual proportionals , the ratio of the first to the

said to be triplicate of the ratio of the first to the second , or of the ratio of the

second to the third , & c . “ So also , if there are five continual proportionals ; the

ratio ...

If four magnitudes are continual proportionals , the ratio of the first to the

**fourth**issaid to be triplicate of the ratio of the first to the second , or of the ratio of the

second to the third , & c . “ So also , if there are five continual proportionals ; the

ratio ...

Side 111

... is to the

of the second rank ; and so on in a cross , or inverse , order ; and the inference is

as in the 19th definition . It is demonstrated in the 23d Prop . of Book 5 . AXIOMS .

... is to the

**fourth**of the first rank , so is the third from the last , to the last but two ,of the second rank ; and so on in a cross , or inverse , order ; and the inference is

as in the 19th definition . It is demonstrated in the 23d Prop . of Book 5 . AXIOMS .

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Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1836 |

Elements of Geometry: Containing the First Six Books of Euclid : with a ... John Playfair Uten tilgangsbegrensning - 1837 |

Elements of Geometry: Containing the First Six Books of Euclid: With a ... John Playfair Uten tilgangsbegrensning - 1854 |

### Vanlige uttrykk og setninger

ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common 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 PROP 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 153 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle...

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 292 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Side 308 - 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 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 78 - To draw a straight line from a given point, either without or in the circumference, which shall touch a given circle. First, let A be a given point without the given circle BCD : it is required to draw a straight line from A which shall touch the circle.

Side 77 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...

Side 39 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the too interior angles upon the same side together equal to two right angles.