## 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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Side 301

If the excess of a magnitude , above a given magnitude , has a

another magnitude ; the excess of both together above a given magnitude shall

have to that other a

above a ...

If the excess of a magnitude , above a given magnitude , has a

**given ratio**toanother magnitude ; the excess of both together above a given magnitude shall

have to that other a

**given ratio**: and if the excess of two magnitudes togetherabove a ...

Side 302

Let the excess of the magnitude AB above a given magnitude have a

to the magnitude BC : the excess of AB above a given magnitude has a

...

Let the excess of the magnitude AB above a given magnitude have a

**given ratio**to the magnitude BC : the excess of AB above a given magnitude has a

**given****ratio**to AC . Let AD be the given magnitude ; and because DB , the excess of AB...

Side 306

EG to FD ; the ratio of EG to FE is given : and GB is given ; therefore EG , the

excess of EB above a given magnitude GB , has a

case is shown in the same way . 0 ad - T 1 PROP . XXIV . 13 . If there be three ...

EG to FD ; the ratio of EG to FE is given : and GB is given ; therefore EG , the

excess of EB above a given magnitude GB , has a

**given ratio**to FD . The othercase is shown in the same way . 0 ad - T 1 PROP . XXIV . 13 . If there be three ...

Side 307

ratio to the second , the same excess shall have a

evident from thd 9th dat . PROP . XXV . 17 , If there be three magnitudes , the

excess of the first whereof above a given magnitude has a

second ...

ratio to the second , the same excess shall have a

**given ratio**to the first ; as isevident from thd 9th dat . PROP . XXV . 17 , If there be three magnitudes , the

excess of the first whereof above a given magnitude has a

**given ratio**to thesecond ...

Side 308

EF , so make CK to LE : therefore the ratio H of CK to LE is given ; and CK is

given , wherefore LE ( 2. dat . ) ... Let AB , C , DE be three magnitudes , and let

the excesses of one of them C above given magnitudes have

EF , so make CK to LE : therefore the ratio H of CK to LE is given ; and CK is

given , wherefore LE ( 2. dat . ) ... Let AB , C , DE be three magnitudes , and let

the excesses of one of them C above given magnitudes have

**given ratios**to AB ...### Hva folk mener - Skriv en omtale

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The Elements of Euclid, Viz; The First Six Books: Together With the Eleventh ... Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2017 |

### 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.