## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of Solids |

### Inni boken

Resultat 1-5 av 22

Side 131

When of the equimultiples of four magnitudes ( taken as in the fifth

multiple of the first is greater than that of the second , but the multiple of the third

is not greater than the multiple of the fourth ; then the first is said to have to the ...

When of the equimultiples of four magnitudes ( taken as in the fifth

**definition**) themultiple of the first is greater than that of the second , but the multiple of the third

is not greater than the multiple of the fourth ; then the first is said to have to the ...

Side 132

... ratio of A to B , and of the ratio of B to C , and of the ratio of C to D ; or the ratio

of A to D is said to be compounded of the ratios of A to B , B to C , and C to D. And

if A : B :: E : F , and B : C :: G : H , and C : D :: K : L , then , since by this

... ratio of A to B , and of the ratio of B to C , and of the ratio of C to D ; or the ratio

of A to D is said to be compounded of the ratios of A to B , B to C , and C to D. And

if A : B :: E : F , and B : C :: G : H , and C : D :: K : L , then , since by this

**definition**... Side 134

... and the inference is as mentioned in the preceding

called ordinate proportion . It is demonstrated in the 22d prop . book 5 . XXI . Ex

æquali , in proportione perturbata , seu inordinata ; from equality , in perturbate ,

or ...

... and the inference is as mentioned in the preceding

**definition**; whence this iscalled ordinate proportion . It is demonstrated in the 22d prop . book 5 . XXI . Ex

æquali , in proportione perturbata , seu inordinata ; from equality , in perturbate ,

or ...

Side 135

and as the third is to the fourth of the first rank , so is the Book V : 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

...

and as the third is to the fourth of the first rank , so is the Book V : 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...

Side 279

necessary to give some account . One of these changes respects the first

or ...

**DEFINITIONS**. I. IN the**definitions**a few changes have been made , of which it isnecessary to give some account . One of these changes respects the first

**definition**, that of a point , which Euclid has said to be , · That which has no parts ,or ...

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Elements of Geometry: Containing the First Six Books of Euclid with a ... John Playfair Uten tilgangsbegrensning - 1855 |

Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclid,John Playfair Uten tilgangsbegrensning - 1853 |

Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1847 |

### Vanlige uttrykk og setninger

ABC is equal ABCD altitude angle ABC angle ACB angle BAC arch base bisected Book centre circle circle ABC circumference coincide common compounded contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equilateral equimultiples exterior angle extremities fall figure fore fourth given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced proportional proposition proved pyramid Q. E. D. PROP ratio reason rectangle contained rectilineal figure right angles segment shown sides similar solid space square taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 121 - 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 42 - 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 63 - Therefore, in obtuse-angled triangles, &c. QED PROP. XIII. THEOREM. In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.

Side 3 - 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 183 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF is the same with the ratio which is compounded •f the ratios of their sides.

Side 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Side 291 - 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 160 - ... extremities of the base shall have the same ratio which the other sides of the triangle have to one...

Side 10 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.

Side 14 - Therefore, upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extretnity equal to one another.