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

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Resultat 1-5 av 56

Side 130

A greater magnitude is said to be a multiple of a less , when the greater is

measured by the less , that is , when the greater contains the less a certain

number of times exactly . III .

same kind ...

A greater magnitude is said to be a multiple of a less , when the greater is

measured by the less , that is , when the greater contains the less a certain

number of times exactly . III .

**Ratio**is a mutual relation of two magnitudes , of thesame kind ...

Side 131

Magnitudes are said to be of the same kind , when the less can be multiplied so

as to exceed the greater ; and it is only such magnitudes that are said to have a

what ...

Magnitudes are said to be of the same kind , when the less can be multiplied so

as to exceed the greater ; and it is only such magnitudes that are said to have a

**ratio**to one another . V. If there be four magnitudes , and if any equimultipleswhat ...

Side 132

X. N. When there is any number of magnitudes of the same kind , the first is said

to have to the last of them the

the second , and of the

X. N. When there is any number of magnitudes of the same kind , the first is said

to have to the last of them the

**ratio**compounded of the**ratio**which the first has tothe second , and of the

**ratio**which the second has to the third , and of the**ratio**... Side 133

If four magnitudes are continual proportionals , the

said to be triplicate of the

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

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

**ratio**... Side 137

IF the first of four magnitudes have the same

has to the fourth , and if any equimultiples whatever be taken of the first and third ,

and any whatever of the second and fourth ; the multiple of the first will have the ...

IF the first of four magnitudes have the same

**ratio**to the second which the thirdhas to the fourth , and if any equimultiples whatever be taken of the first and third ,

and any whatever of the second and fourth ; the multiple of the first will have the ...

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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.