## The Elements of Euclid: 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. viz. the first six books, together with the eleventh and twelfth |

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Resultat 1-5 av 8

Side 237

which has length , breadth , and thickness , in order to understand aright the

exist in ...

**DEFINITION**I. BOOK I. It is necessary to consider a solid , that is , a magnitudewhich has length , breadth , and thickness , in order to understand aright the

**definitions**of a point , line , and superficies ; for these all arise from a solid , andexist in ...

Side 249

in the 1st , 2d , 3d , and 6th

must be read instead of “ contingit ; " and in the 2d and 3d

the same change must be made : but in the Greek text of propositions 11th , 12th

...

in the 1st , 2d , 3d , and 6th

**definitions**in Commandine's translation , “ tangit , "must be read instead of “ contingit ; " and in the 2d and 3d

**definitions**of book 3 ,the same change must be made : but in the Greek text of propositions 11th , 12th

...

Side 250

B. V. It was necessary to add the word “ continual ” before “ proportionals " in this

ought to have followed the

B. V. It was necessary to add the word “ continual ” before “ proportionals " in this

**definition**; and thus it is cited in the 33d próp . of book 11 . After this**definition**ought to have followed the

**definition**of compound ratio , as this was the proper ... Side 262

Besides , that there is not the least mention made of this

of Euclid , Archimedes , Apollonius , or other ancients , though they frequently

make use of compound ratio ; and in this 23d prop . of the 6th book , where ...

Besides , that there is not the least mention made of this

**definition**in the writingsof Euclid , Archimedes , Apollonius , or other ancients , though they frequently

make use of compound ratio ; and in this 23d prop . of the 6th book , where ...

Side 265

... explication of the meaning of these ratios is plain from the

duplicate and triplicate ratio , in which Euclid makes use of the word nɛyɛtai , is

said to be , or is called , which word , he , no doubt , made use of also in the

... explication of the meaning of these ratios is plain from the

**definitions**ofduplicate and triplicate ratio , in which Euclid makes use of the word nɛyɛtai , is

said to be , or is called , which word , he , no doubt , made use of also in 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: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1892 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone contained 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 gles greater Greek half join less likewise 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 45 - Ir 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 41 - 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 54 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.

Side 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.

Side 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.

Side 8 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 256 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Side 129 - 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 23 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...

Side 20 - ANY two angles of a triangle are together less than two right angles.