## 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 |

### Inni boken

Resultat 1-5 av 6

Side 27

these add the

than the

; therefore the

these add the

**angle ACB**; therefore the angles ACD , ACB are Book I. greaterthan the

**angles ABC**, ACB ; but ACD , ACB are together equal to two right angles; therefore the

**angles ABC**, b 13. 1 . BCA are less than two right angles . Side 104

Let ABC be the given circle , and DEF the given triangle ; it is required to inscribe

in the circle ABC a triangle ... HAC is equalc to the

segment of the circle : but HAC is equal to the angle DEF ; therefore also the

angle ...

Let ABC be the given circle , and DEF the given triangle ; it is required to inscribe

in the circle ABC a triangle ... HAC is equalc to the

**angle ABC**in the alternatesegment of the circle : but HAC is equal to the angle DEF ; therefore also the

angle ...

Side 400

IF a triangle has one of its angles which is not a right angle given , and if the

sides about another angle have a given ratio to one another ; the triangle is given

in species . A Let the

IF a triangle has one of its angles which is not a right angle given , and if the

sides about another angle have a given ratio to one another ; the triangle is given

in species . A Let the

**triangle ABC**have one of its**angles ABC**a gires , but not a ... Side 426

IF a triangle has a given obtuse angle ; the excess of the square of the side which

subtends the obtuse angle , above the squares of the sides which contain it ,

shall have a given ratio to the triangle . Let the

...

IF a triangle has a given obtuse angle ; the excess of the square of the side which

subtends the obtuse angle , above the squares of the sides which contain it ,

shall have a given ratio to the triangle . Let the

**triangle ABC**have a given obtuse...

Side 460

And because the straight line F.FG is drawn from a piven point F without or within

the circle

position ; and from this point a straight line be drawn making with the first an

And because the straight line F.FG is drawn from a piven point F without or within

the circle

**ABC**given in position, d 'J5. ... the circumference of a circle given inposition ; and from this point a straight line be drawn making with the first an

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### Andre utgaver - Vis alle

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

The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2015 |

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.