## 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 231

another as their bases . ... are the points G , H , be of the same altitude : as the

base ABC to the base DEF , so shall the

**Pyramids**of the same altitude which have triangular See N. bases , are to oneanother as their bases . ... are the points G , H , be of the same altitude : as the

base ABC to the base DEF , so shall the

**pyramid**ABCG be to the**pyramid**DEFH . Side 232

5 . the base ABC be to the base DEF , as the

greater than the

, the solid Z. And because the base ABC is to the base DEF as the

5 . the base ABC be to the base DEF , as the

**pyramid**ABCG to any solid which isgreater than the

**pyramid**DEFH . For , if it be possible , let it be so to a greater , viz, the solid Z. And because the base ABC is to the base DEF as the

**pyramid**... Side 233

M N DF AS G H * 5 . ing bases as many

the point N. Therefore since the triangle ABC is to the triangle FGH , as * the

triangle ...

M N DF AS G H * 5 . ing bases as many

**pyramids**having their common vertex inthe point N. Therefore since the triangle ABC is to the triangle FGH , as * the

**pyramid**ABCM to * 5. 12 . the**pyramid**FGHN ; and the triangle ACD to thetriangle ...

Side 237

Again , let the bases and altitudes of the

proportional , viz . the base ABC to the ... the altitude of the

altitude of the

Again , let the bases and altitudes of the

**pyramids**ABCG , DEFH , be reciprocallyproportional , viz . the base ABC to the ... the altitude of the

**pyramid**DEFH to thealtitude of the

**pyramid**ABCG : the**pyramid**ABCG shall be equal to the**pyramid**... Side 329

M. N E K L H А B similar to one another : therefore the

triangles EAB , LFG , for their bases , and the ... B . 11 . solids themselves are

contained by the same number of similar planes : in the same manner the

M. N E K L H А B similar to one another : therefore the

**pyramids**which have thetriangles EAB , LFG , for their bases , and the ... B . 11 . solids themselves are

contained by the same number of similar planes : in the same manner the

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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.