## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. The first six books, together with the eleventh and twelfth |

### Inni boken

Resultat 1-5 av 8

Side 52

1 . equal to the squares of EG , GF ; therefore the square of EF is

square GF . and GF is equal h to CD ; therefore the square of EF is

square of CD . but the square of E AE is likewise

1 . equal to the squares of EG , GF ; therefore the square of EF is

**double**of thesquare GF . and GF is equal h to CD ; therefore the square of EF is

**double**of thesquare of CD . but the square of E AE is likewise

**double**of the square of AC ... Side 53

1 , to the squares of EC , CA ; therefore the square of EA is

of AC . again , because GF is equal to FE , the square of GF is equal to the

square of FE ; and therefore the squares of GF , FE are

EF . but ...

1 , to the squares of EC , CA ; therefore the square of EA is

**double**of the squareof AC . again , because GF is equal to FE , the square of GF is equal to the

square of FE ; and therefore the squares of GF , FE are

**double**of the square ofEF . but ...

Side 77

Let ABC be a circle , and BEC an angle at the center , and BAC Book III . an

angle at the circumference , which have the same circumference BC for their

base ; the angle BEC is

circle ...

Let ABC be a circle , and BEC an angle at the center , and BAC Book III . an

angle at the circumference , which have the same circumference BC for their

base ; the angle BEC is

**double**А. of the angle BAC . First , Let E the center of thecircle ...

Side 103

1 . the angle DAC . therefore the angles CDA , DAC together , are

angle DAC . but BCD is equal to the angies CDA , DAC ; therefore also BCD is

therefore ...

1 . the angle DAC . therefore the angles CDA , DAC together , are

**double**of theangle DAC . but BCD is equal to the angies CDA , DAC ; therefore also BCD is

**double**of DAC . and BCD is equal to each of the angles BDA , DBA ; eachtherefore ...

Side 105

KFC , and the angle BKF to FKC . wherefore the angle BFC is

KFC , and BKC

the angle CFL , and CLD

KFC , and the angle BKF to FKC . wherefore the angle BFC is

**double**of the angleKFC , and BKC

**double**of FKC . for the fame reason , the angle CFD is**double**ofthe angle CFL , and CLD

**double**of CLF . and because the circumference BC is ...### Hva folk mener - Skriv en omtale

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### Andre utgaver - Vis alle

The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ... Robert Simson Uten tilgangsbegrensning - 1775 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1762 |

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... Robert Simson Uten tilgangsbegrensning - 1827 |

### Vanlige uttrykk og setninger

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### Populære avsnitt

Side 156 - 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 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 323 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 92 - If from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square- of the line which meets it, the line which meets shall touch the circle.

Side 80 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.

Side 52 - If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced.

Side 36 - 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 2 - 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 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.

Side 74 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...