## 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

Side 301

If the excess of a magnitude , above a

another magnitude ; the excess of both together above a

have to that other a given ratio : and if the excess of two magnitudes together

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**shallhave to that other a given ratio : and if the excess of two magnitudes together

above a ...

Side 302

Let the excess of the magnitude AB above a

to the magnitude BC : the excess of AB above a

ratio to AC . Let AD be the

...

Let the excess of the magnitude AB above a

**given magnitude**have a given ratioto the magnitude BC : the excess of AB above a

**given magnitude**has a givenratio to AC . Let AD be the

**given magnitude**; and because DB , the excess of AB...

Side 304

In the EB above a

the other case is demonstrated . PROP . XX . 16 . IF to one of two magnitudes

which have a given ratio to one another , a

the ...

In the EB above a

**given magnitude**EG , has a given ratio to FD . same mannerthe other case is demonstrated . PROP . XX . 16 . IF to one of two magnitudes

which have a given ratio to one another , a

**given magnitude**be added , and fromthe ...

Side 307

ratio to the second , the same excess shall have a given ratio to the first ; as is

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

excess of the first whereof above a

second ...

ratio to the second , the same excess shall have a given ratio to the first ; as is

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 given ratio to thesecond ...

Side 308

the ratio of HB to LF is given : and from HB , LF the

being taken , the remainders A D F AB , EF shall either have a given ratio to one

another , or the excess of one of them above a

to ...

the ratio of HB to LF is given : and from HB , LF the

**given magnitudes**HA , LEbeing taken , the remainders A D F AB , EF shall either have a given ratio to one

another , or the excess of one of them above a

**given magnitude**has a given ratioto ...

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

### 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.