## 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 9

Side 26

For if it be not parallel , AB and CD being produced shall

or towards AC . let them be produced and

therefore GEF is a triangle , and its exterior angle AEF is greater than the interior

and ...

For if it be not parallel , AB and CD being produced shall

**meet**either towards BDor towards AC . let them be produced and

**meet**towards BD in the point G ;therefore GEF is a triangle , and its exterior angle AEF is greater than the interior

and ...

Side 52

31.1 . it equal to AC or CB , and join AE , EB ; thro'E draw 6 EF parallel to AB ,

and thrơ D draw DF parallel to CE . and because the straight line EF

parallels EC , FD , the angles CEF , EFD are equal to two right angles ; and

therefore ...

31.1 . it equal to AC or CB , and join AE , EB ; thro'E draw 6 EF parallel to AB ,

and thrơ D draw DF parallel to CE . and because the straight line EF

**meets**theparallels EC , FD , the angles CEF , EFD are equal to two right angles ; and

therefore ...

Side 201

F two straight lines meeting one another , be parallel Sce N. to two straight lines

which

plane which passes through these is parallel to the plane passing through the

others ...

F two straight lines meeting one another , be parallel Sce N. to two straight lines

which

**meet**one another , but are not in the same plane with the first two ; theplane which passes through these is parallel to the plane passing through the

others ...

Side 202

For , if it is not , EF , GH shall

first , let them be produced on the side of TH , and

since EFK is in the piane Ab , every point in EFK is in that plane ; and K is a point

...

For , if it is not , EF , GH shall

**meet**, if produced , either on the side of FH , or LG .first , let them be produced on the side of TH , and

**meet**in the point K. thereforesince EFK is in the piane Ab , every point in EFK is in that plane ; and K is a point

...

Side 293

... described from the center F , at the distance FD , must

, DM FG H because FD is less than FH ; and that , for the like reason , the circle

described from the center G , at the distance GH or GM must

... described from the center F , at the distance FD , must

**meet**FH betwixt F and H, DM FG H because FD is less than FH ; and that , for the like reason , the circle

described from the center G , at the distance GH or GM must

**meet**DG betwixt D ...### 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...