## The Elements of Euclid: The Errors by which Theon, Or Others, Have Long 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 |

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Side 39

From the point A draw * AD at right angles to AC , 1. 1 . and maket AD equal to

BA , and join DC . Then , + 3. 1 . because DA is equal to AB , the square of DA is

equal to the square of AB : to each of these add the

From the point A draw * AD at right angles to AC , 1. 1 . and maket AD equal to

BA , and join DC . Then , + 3. 1 . because DA is equal to AB , the square of DA is

equal to the square of AB : to each of these add the

**square of AC**; therefore the ... Side 48

And because AC is equal to CE , the

therefore the

of AE is equal * to the

And because AC is equal to CE , the

**square of ĄC**is equal to the square of CE ;therefore the

**squares of AC**, CE , are double of the**square of AC**: but the squareof AE is equal * to the

**squares of AC**, CE because ACE is a right angle ... Side 49

CA ; therefore the square of EA is double of the

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 of EF : but the square of EG is

equal ...

CA ; therefore the square of EA is double of the

**square of AC**: again , becauseGF 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 of EF : but the square of EG is

equal ...

Side 52

AD , DC : but the square of AB is equal * to the squares of BD , DA , because the

angle BDA is a right angle ; and the

DC ; therefore the squares of CB , BA are equal to the

AD , DC : but the square of AB is equal * to the squares of BD , DA , because the

angle BDA is a right angle ; and the

**square of AC**is equal to the squares of AD ,DC ; therefore the squares of CB , BA are equal to the

**square of AC**, and twice ... Side 421

HL But if twice the given rectangle be not equal to the given sum of the squares of

the sides , it must be less than it , as ... because the sum of the squares of AB , BC

is given , the

HL But if twice the given rectangle be not equal to the given sum of the squares of

the sides , it must be less than it , as ... because the sum of the squares of AB , BC

is given , the

**square of AC**which is equal to that sum is given ; and AC * 47.### Hva folk mener - Skriv en omtale

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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 Ago ... Robert Simson Uten tilgangsbegrensning - 1781 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid excess figure fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition proved pyramid radius reason rectangle rectilineal figure remaining right angles segment shewn sides similar sine solid sphere square square of AC taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 141 - 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 40 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...

Side 26 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another, and the exterior angle equal to the interior and opposite upon the same side, and also the two interior angles upon the same side together equal to two right angles.

Side 46 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Side 28 - Cor. angles; that is * together with four right angles. There1s, 1. fore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 21 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.

Side 12 - IF two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise their bases equal; the angle. which is contained by the two sides...

Side 169 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.

Side 5 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre.

Side 97 - 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.