## 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 5

Side 92

To inscribe an equilateral and

ABCD be the given circle ; it is required to inscribe an equilateral and

equilateral triangle ...

To inscribe an equilateral and

**equiangular**quindecagon , in a given circle . * LetABCD be the given circle ; it is required to inscribe an equilateral and

**equiangular**quindecagon in the circle ABCD . Let AC be the side of anequilateral triangle ...

Side 129

and the triangle ABC is therefore ES F

consequently they have their sides opposite to the B с equal angles proportionals

( 4 . G 6. ) . Wherefore , as AB to BC , so is GE to EF ; but as AB to BC , so is DE to

...

and the triangle ABC is therefore ES F

**equiangular**to the triangle GEF ; andconsequently they have their sides opposite to the B с equal angles proportionals

( 4 . G 6. ) . Wherefore , as AB to BC , so is GE to EF ; but as AB to BC , so is DE to

...

Side 131

Next , let each of the angles at C , F , be not less than a right angle : the triangle

ABC is also in this case

being A made , it may be proved in like D manner that BC is equal to BG , and the

...

Next , let each of the angles at C , F , be not less than a right angle : the triangle

ABC is also in this case

**equiangular**to the triangle DEF . The same constructionbeing A made , it may be proved in like D manner that BC is equal to BG , and the

...

Side 138

the angle BGH equal to the angle DFE , and the angle GBH equal to FDE : K

therefore the remaining angle FED is equal to the re- A B С D maining angle

GHB ; and the triangle FDE

angle ...

the angle BGH equal to the angle DFE , and the angle GBH equal to FDE : K

therefore the remaining angle FED is equal to the re- A B С D maining angle

GHB ; and the triangle FDE

**equiangular**to the triangle GBH : then , because theangle ...

Side 335

to BL ; therefore the ratio of BL to EG is given : and because BL is

EG , and , by the hypothesis , the ratio of BC to FG is given ; therefore ( 65. dat . )

the ratio of KB to EF is given , and the A K D L ratio of KB to BA is given ; the ratio

...

to BL ; therefore the ratio of BL to EG is given : and because BL is

**equiangular**toEG , and , by the hypothesis , the ratio of BC to FG is given ; therefore ( 65. dat . )

the ratio of KB to EF is given , and the A K D L ratio of KB to BA is given ; the ratio

...

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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.