## 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 twelfthMathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 - 518 sider |

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Resultat 1-5 av 6

Side 344

But if B and C together be less than A ; then , because it is required that B , C , D

together be greater than A , from each of these taking away B , C , the remaining

one D must be greater than the

But if B and C together be less than A ; then , because it is required that B , C , D

together be greater than A , from each of these taking away B , C , the remaining

one D must be greater than the

**excess**of A above B and C : take therefore any ... Side 377

Let AD be the given magnitude , the

given ratio A D в с to BC : and because DB has a given ratio to BC , the ratio of

DC to CB is given a , and AD is given ; therefore DC , the

Let AD be the given magnitude , the

**excess**of AB above which , viz . DB has agiven ratio A D в с to BC : and because DB has a given ratio to BC , the ratio of

DC to CB is given a , and AD is given ; therefore DC , the

**excess**of a 7. dat , AC ... Side 383

5 . given ; therefore EG , the

given ratio to FD . The other case is shown in the same way . PROP . XXIV . 13 .

IF there be three magnitudes , the first of which See N. has a given ratio to the ...

5 . given ; therefore EG , the

**excess**of EB above a given magnitude GB , has agiven ratio to FD . The other case is shown in the same way . PROP . XXIV . 13 .

IF there be three magnitudes , the first of which See N. has a given ratio to the ...

Side 384

Also , if the first has a given ratio to the second , and the

a given magnitude has also a gira ratio to the second , the same

have a given ratio m the first ; as is evident from the 9th dat . 17 . PROP . XXV .

Also , if the first has a given ratio to the second , and the

**excess**of the third abovea given magnitude has also a gira ratio to the second , the same

**excess**shallhave a given ratio m the first ; as is evident from the 9th dat . 17 . PROP . XXV .

Side 386

If there be three magnitudes , the

magnitude has a given ratio to the second ; and the

a given magnitude has also a given ratio to the third : the

a ...

If there be three magnitudes , the

**excess**of the first of which above a givenmagnitude has a given ratio to the second ; and the

**excess**of the second abovea given magnitude has also a given ratio to the third : the

**excess**of the first abovea ...

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The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

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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

ABCD added altitude angle ABC angle BAC base Book centre circle circle ABC circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prisms produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained 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 30 - Any two sides of a triangle are together greater than the third side.

Side 64 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.

Side 30 - IF, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. Let...

Side 59 - PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour 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 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.

Side 165 - 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 19 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.

Side 191 - In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle.

Side 39 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.

Side 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.