## 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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Side vi

Also the Note on the 29th Proposition, Book 1st, is altered, and made more

explicit, and a more general Demonstration is given, instead of that which was in

the Note on the 10th

Also the Note on the 29th Proposition, Book 1st, is altered, and made more

explicit, and a more general Demonstration is given, instead of that which was in

the Note on the 10th

**Definition**of Book 11th ; besides, the Translation is much ... Side 296

And in this manner the

understood . B. DEF . VII . B. I. Instead of this

, a more distinct one is given from a property of a plane superficies , which is ...

And in this manner the

**definitions**of a point , line , and superficies , are to beunderstood . B. DEF . VII . B. I. Instead of this

**definition**as it is in the Greek copies, a more distinct one is given from a property of a plane superficies , which is ...

Side 297

B. I. The words , “ which also divides the circle into two equal parts , " are added

at the end of this

to the

B. I. The words , “ which also divides the circle into two equal parts , " are added

at the end of this

**definition**in all the copies , but are now left out as not belongingto the

**definition**, being only a corollary from it . Proclus demonstrates it by ... Side 311

To this citation from Dr. Barrow I have nothing to add , except that I fully believe

the 3d and 8th

continual ” before " proportionals ” in this

prop ...

To this citation from Dr. Barrow I have nothing to add , except that I fully believe

the 3d and 8th

**definitions**are not ... B. V. It was necessary to add the word “continual ” before " proportionals ” in this

**definition**; and thus it is cited in the 33dprop ...

Side 326

Theon's

λογων πηλικοτητες εφ ' εαυτας πολλαπλα . ... Dr. Gregory renders the last words

of the

...

Theon's

**definition**is this : a ratio is said to be compounded of ratios οταν αι τωνλογων πηλικοτητες εφ ' εαυτας πολλαπλα . ... Dr. Gregory renders the last words

of the

**definition**by illius facit quantitatem , ” makes the quantity of that ratio ; but in...

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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.