## 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 13

Side 112

3. angle BAE is equal f to the angle AED : for the same

angles ABC , BCD , CDE is equal to the angle BAE , or AED : therefore the

pentagon ABCDE is equiangular ; and it has been shown that it is equilateral .

Wherefore ...

3. angle BAE is equal f to the angle AED : for the same

**reason**, each of theangles ABC , BCD , CDE is equal to the angle BAE , or AED : therefore the

pentagon ABCDE is equiangular ; and it has been shown that it is equilateral .

Wherefore ...

Side 162

5 . the same ratio to EF , and consequently are equal e : for the same

is equal to FG : and because in the triangles DEF , GEF , DE is equal to EG , and

EF common , the two sides DE , EF are equal to the two GE , EF , and the base ...

5 . the same ratio to EF , and consequently are equal e : for the same

**reason**, DFis equal to FG : and because in the triangles DEF , GEF , DE is equal to EG , and

EF common , the two sides DE , EF are equal to the two GE , EF , and the base ...

Side 177

6 . has to the side GL : for the same

duplicate ratio of that which BE has to GL : therefore , as the triangle ABE to the

triangle FGL , so f is the trian- f 11. 5 . gle BEC to the triangle GLH . Again ,

because ...

6 . has to the side GL : for the same

**reason**, the triangle BEC has to GLH theduplicate ratio of that which BE has to GL : therefore , as the triangle ABE to the

triangle FGL , so f is the trian- f 11. 5 . gle BEC to the triangle GLH . Again ,

because ...

Side 193

3 . and the triangle BGC is equal to the triangle CGK ; therefore the whole , the

sector BGC , is equal to the whole , the sector CGK : for the same

sector KGL is equal to each of the sectors BGC , CGK : in the same manner , the ...

3 . and the triangle BGC is equal to the triangle CGK ; therefore the whole , the

sector BGC , is equal to the whole , the sector CGK : for the same

**reason**, thesector KGL is equal to each of the sectors BGC , CGK : in the same manner , the ...

Side 201

equal to EH , and AG to BH : and because AE is equal to EB , Book XI . and FE

common and at right angles to them , the base AF is an equal b to the base FB ;

for the same

equal to EH , and AG to BH : and because AE is equal to EB , Book XI . and FE

common and at right angles to them , the base AF is an equal b to the base FB ;

for the same

**reason**, CF is equal to FD : b 4. 1 . and because AD is equal to BC ...### Hva folk mener - Skriv en omtale

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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 Ingen forhåndsvisning tilgjengelig - 2017 |

### Vanlige uttrykk og setninger

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### 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.