## 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 twelfthA. Foulis, 1781 - 466 páginas |

### Dentro del libro

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Página 40

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**square**upon a given straight line . Let AB be the given straight line ; it is required to describe a fquare upon AB . d c From the point A draw a**AC**at right angles to AB ; and make b AD equal to AB , and thro ' the point D draw DE ... Página 41

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**square**BDEC is equal to the two fquares GB , HC . and the**square**BDEC is described upon the ftraight line BC , and the fquares GB , HC upon BA ,**AC**. wherefore the fquare upon the fide BC is equal to the**squares**upon the fides BA ,**AC**... Página 45

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**AC**; for it is contained by Book II . DA ,**AC**, of which AD is equal to AB ; and CE is contained by AB , BC , for BE ...**square**of BC . If therefore a straight line , & c . Q. E. D. FD E PROP . IV . THEO R. IF a straight line be divided into ... Página 49

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**AC**. a Upon AB describe the**square**ADEB , and construct the figure a 46. 1 . as in the preceding Propofitions . and because AG is equal to GE , b . 43. l . add to each of them CK , the whole AK is therefore equal to the c A C B G K c ... Página 51

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**square**of the line between the points of fection . Let the ftraight line AB be divided at the point C into two equal , and at D into two unequal parts . the fquares of AD , DB are together double of the fquares of**AC**, CD . A 51 Book II ...### Otras ediciones - Ver todas

### Términos y frases comunes

AC is equal alfo alſo angle ABC angle BAC bafe baſe BC is given becauſe the angle bifected Book XI cafe circle ABCD circumference cone confequently cylinder defcribed demonftrated diameter drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fecond fegment fhall fhewn fide BC fides fimilar fince firft firſt folid angle fome fore fquare of AC ftraight line AB given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs leſs likewife line BC muſt oppofite parallel parallelepipeds parallelogram perpendicular prifm Propofition proportionals pyramid rectangle contained rectilineal figure right angles ſhall ſphere ſquare thefe THEOR theſe thro tiple triangle ABC vertex wherefore

### Pasajes populares

Página 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.

Página 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.

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

Página 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.

Página 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.

Página 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.

Página 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.

Página 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.

Página 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.

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