## 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 6-10 av 12

Side 213

... the angles E H KAD , MBG are equal , as also the right angles AKD , BMG , and

that the sides AK , PM , adjacent to the equal angles , are equal to one another ,

therefore KD is equal o to MG , and AD to BG . for the same

... the angles E H KAD , MBG are equal , as also the right angles AKD , BMG , and

that the sides AK , PM , adjacent to the equal angles , are equal to one another ,

therefore KD is equal o to MG , and AD to BG . for the same

**reason**, in the b . Side 218

Book XI . multiplc soever the base LF is of the base AF , the fame multiple is the

solid LV of the solid AV . for the same

of the base HF , the fame multiple is the folid NV of the folid ED . and if the bafe

LF ...

Book XI . multiplc soever the base LF is of the base AF , the fame multiple is the

solid LV of the solid AV . for the same

**reason**, whatever multiple the base NF isof the base HF , the fame multiple is the folid NV of the folid ED . and if the bafe

LF ...

Side 228

... by

similar and equal to the parallelogram CN . for the same

parallelogram MK is similar and equal to CR , and also OE to FD . therefore three

...

... by

**reason**that the folids AB , • CD are limilar ; therefore the parallelogram KL issimilar and equal to the parallelogram CN . for the same

**reason**, theparallelogram MK is similar and equal to CR , and also OE to FD . therefore three

...

Side 279

... to AB the common fection of the planes , therefore OV is perpendicular d to the

plane BCDE . for the same day Def.nr.

plane , because the plane KSXN is at right angles to the plane BCDE . Join VQ ...

... to AB the common fection of the planes , therefore OV is perpendicular d to the

plane BCDE . for the same day Def.nr.

**reason**SQ is perpendicular to the fameplane , because the plane KSXN is at right angles to the plane BCDE . Join VQ ...

Side 280

... it may be demonstrated that TP is parallel to KB in the very fame way that SO

was shewn to be parallel to the fame K5 ; wherefore h TP is parallel to SO , and

the quadilateral figure SOPT is in one plane . for the same

quadrilateral ...

... it may be demonstrated that TP is parallel to KB in the very fame way that SO

was shewn to be parallel to the fame K5 ; wherefore h TP is parallel to SO , and

the quadilateral figure SOPT is in one plane . for the same

**reason**thequadrilateral ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### 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

added alſo altitude angle ABC angle BAC baſe becauſe Book caſe circle circle ABCD circumference common cone cylinder Definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs fame fides figure firſt folid angle fore four fourth given angle given in poſition given magnitude given ratio given ſtraight line greater half join leſs likewiſe magnitude manner meet multiple muſt oppoſite parallel parallelogram perpendicular plane produced PROP proportionals Propoſition pyramid radius reaſon rectangle rectangle contained rectilineal remaining right angles ſame ſecond ſegment ſhall ſides ſimilar ſolid ſphere ſquare ſquare of AC taken THEOR theſe third thro triangle ABC wherefore whole

### 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...