## 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 7

Side 240

13 , book 1. This part must therefore have been

of some proposition betwixt the 5th and 13th , but none of these stand in need of

it except the 7th proposition , on account of which it has been

13 , book 1. This part must therefore have been

**added**to prop . 5 , upon accountof some proposition betwixt the 5th and 13th , but none of these stand in need of

it except the 7th proposition , on account of which it has been

**added**: besides ... Side 241

... which he bids take from GF , may be greater than it , as in the figure here

annexed : in which case bis demonstration must be changed into another . now

und finis To this is

greater ...

... which he bids take from GF , may be greater than it , as in the figure here

annexed : in which case bis demonstration must be changed into another . now

und finis To this is

**added**, “ of the two sides DE , DF , let DE be that which is notgreater ...

Side 250

... nothing to add , except that I fully believe the 3d and 8th definitions are not

Euclid's , but

add the word “ continual ” before “ proportionals " in this definition ; and thus it is

cited ...

... nothing to add , except that I fully believe the 3d and 8th definitions are not

Euclid's , but

**added**by some unskilful editor . DEF . XI . B. V. It was necessary toadd the word “ continual ” before “ proportionals " in this definition ; and thus it is

cited ...

Side 304

IF to one of two magnitudes which have a given ratio to one another , a given

magnitude be

excess of the sum above a given magnitude shall have a given ratio to the

remainder .

IF to one of two magnitudes which have a given ratio to one another , a given

magnitude be

**added**, and from the other a given magnitude be taken ; theexcess of the sum above a given magnitude shall have a given ratio to the

remainder .

Side 375

Each of these has a determination , which is now

change in their demonstrations . PROP . XXXVII . XXXIX . XL . XLI . The 35th and

36th propositions in the Greek text are joined into one , which makes the 39th in

this ...

Each of these has a determination , which is now

**added**, which occasions achange in their demonstrations . PROP . XXXVII . XXXIX . XL . XLI . The 35th and

36th propositions in the Greek text are joined into one , which makes the 39th in

this ...

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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.