## 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 65

1 . bisecting BD at right angles : therefore , because the points B , D , are in the

circumference of each of the

therefore one

1 . bisecting BD at right angles : therefore , because the points B , D , are in the

circumference of each of the

**circles**, the ... the straight line GH ; which is absurd :therefore one

**circle**cannot touch another on the inside in more points than one . Side 86

tilineal figure , when the circumference of the

figure . VI . ecA

circumference of the

about ...

tilineal figure , when the circumference of the

**circle**touches each side of thefigure . VI . ecA

**circle**is said to be described about a tilineal figure , when thecircumference of the

**circle**passes through all the angular points of the figureabout ...

Side 224

See N.

. Let ABCD , EFGH be two

BD to the square of FH , so shall the

See N.

**Circles**are to one another as the squares of their diameters . + 6.4 . * 41.1. Let ABCD , EFGH be two

**circles**, and BD , FH their diameters : as the square ofBD to the square of FH , so shall the

**circle**ABCD be to the**circle**EFGH . Side 226

5 . as ABCD : but as the space T is to the

some space , which must be less * than the

greater , by hypothesis , than the

...

5 . as ABCD : but as the space T is to the

**circle**ABCD , so is the**circle**EFGH tosome space , which must be less * than the

**circle**ABCD , because the space T isgreater , by hypothesis , than the

**circle**EFGH ; therefore as the square of FH is to...

Side 243

In the same manner it may be demonstrated , that the

cone ...

In the same manner it may be demonstrated , that the

**circle**EFGH is not to the**circle**ABCD , as the cone EN to any solid less than the cone AL . Nor can the**circle**ABCD be to the**circle**EFGH , as the cone AL , to any solid greater than thecone ...

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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.