## The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; 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 |

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Resultat 1-5 av 12

Side 26

not ; therefore the

equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c .

Q. E. D. PROP . XX . THEOR . Any two

not ; therefore the

**side**AC is not less than AB ; and it has been shown that it is notequal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c .

Q. E. D. PROP . XX . THEOR . Any two

**sides**of a triangle are together greater ... Side 29

Of the two

and at the point D , in the straight line DE , make ( 23. 1. ) the angle EDG equal to

the angle BAC ; and make DG equal ( 3. 1. ) to AC or DF , and join EG , GF .

Of the two

**sides**DE , DF , let DE be the**side**which is not greater than the other ,and at the point D , in the straight line DE , make ( 23. 1. ) the angle EDG equal to

the angle BAC ; and make DG equal ( 3. 1. ) to AC or DF , and join EG , GF .

Side 289

11. ) to one another , each to each : but similar pyramids have to one another the

triplicate ( Cor . 8. 12. ) ratio of their homologous

which the base is the quadrilateral KBOS , and vertex A , has to the pyramid in ...

11. ) to one another , each to each : but similar pyramids have to one another the

triplicate ( Cor . 8. 12. ) ratio of their homologous

**sides**. Therefore the pyramid ofwhich the base is the quadrilateral KBOS , and vertex A , has to the pyramid in ...

Side 297

B. I. This definition has one condition more than is necessary ; because every

quadrilateral figure which has its opposite

likewise its opposite angles equal , and on the contrary . Let ABCD be a

quadrilateral ...

B. I. This definition has one condition more than is necessary ; because every

quadrilateral figure which has its opposite

**sides**equal to one another , haslikewise its opposite angles equal , and on the contrary . Let ABCD be a

quadrilateral ...

Side 329

... ratios of the

: if there be two equiangular parallelograms ... the ratio which is the same with

that which is compounded of ratios that are the same with the ratios of the

... ratios of the

**sides**, and by this they expressed the proposition more briefly thus: if there be two equiangular parallelograms ... the ratio which is the same with

that which is compounded of ratios that are the same with the ratios of the

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Euclid,Robert Simson Uten tilgangsbegrensning - 1838 |

### Vanlige uttrykk og setninger

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

### Populære avsnitt

Side 9 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 81 - The angles in the same segment of a circle are equal to one another.

Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Side 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 155 - 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 22 - ANY two angles of a triangle are together less than two right angles.

Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.

Side 24 - Any two sides of a triangle are together greater than the third side.