## 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 |

### Inni boken

Resultat 1-5 av 10

Side 249

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

...

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 257

... certain conclusion can never be deduced by the means of an uncertain

proposition : upon this account , we have given a legitimate demonstration of this

proposition instead of that in the

Theon ...

... certain conclusion can never be deduced by the means of an uncertain

proposition : upon this account , we have given a legitimate demonstration of this

proposition instead of that in the

**Greek**and other editions , which very probablyTheon ...

Side 281

... again into two others , one of which is , when the bases are equiangular

parallelograms ; the other , when they are not equiangular : the

makes no mention of the first of these two last cases , but has inserted the

demonstration of ...

... again into two others , one of which is , when the bases are equiangular

parallelograms ; the other , when they are not equiangular : the

**Greek**editormakes no mention of the first of these two last cases , but has inserted the

demonstration of ...

Side 291

... that the compositions of problems solved by help of the Data may be the more

easily made . Marinus the philosopher's preface , which , in the

prefixed to the Data , is here left out , as being of no use to understand them ...

... that the compositions of problems solved by help of the Data may be the more

easily made . Marinus the philosopher's preface , which , in the

**Greek**editions , isprefixed to the Data , is here left out , as being of no use to understand them ...

Side 361

The analysis of this problem might have been made as in the 86th prop . in the

this edition . PROP . XC . 0 . If two straight lines contain a given parallelogram in

a ...

The analysis of this problem might have been made as in the 86th prop . in the

**Greek**, and the composition of it may be made as that which is in prop . 87th ofthis edition . PROP . XC . 0 . If two straight lines contain a given parallelogram in

a ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

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.