## 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

Side 25

And , in like manner , it may be demonstrated , that no other can be in the same

straight line with it but BD , which therefore is in the same straight line with CB .

Wherefore , if at a point , & c . Q. E. D. PROP . XV .

cut ...

And , in like manner , it may be demonstrated , that no other can be in the same

straight line with it but BD , which therefore is in the same straight line with CB .

Wherefore , if at a point , & c . Q. E. D. PROP . XV .

**THEOR**. IF two straight linescut ...

Side 130

C.

part of it , that the third is of the fourth ; the first is to the second as the third is to

the fourth . G F H Let the first A be the same multiple of B the second , that C the

third ...

C.

**THEOR**. See N. If the first be the same multiple of the second , or the samepart of it , that the third is of the fourth ; the first is to the second as the third is to

the fourth . G F H Let the first A be the same multiple of B the second , that C the

third ...

Side 161

proportionals ; and those which are opposite to the equal angles are homologous

sides , that is , are the antecedents or consequents of the ratios . Let ABC , DCE

be ...

**THEOR**. THE sides about the equal angles of equiangular triangles areproportionals ; and those which are opposite to the equal angles are homologous

sides , that is , are the antecedents or consequents of the ratios . Let ABC , DCE

be ...

Side 162

PROP . V.

proportionals , the triangles shall be equiangular , and have their equal angles

opposite to the homologous sides . A Let the triangles ABC , DEF have their sides

...

PROP . V.

**THEOR**. IF the sides of two triangles , about each of their angles , beproportionals , the triangles shall be equiangular , and have their equal angles

opposite to the homologous sides . A Let the triangles ABC , DEF have their sides

...

Side 199

I.

part above it . If it be possible , let AB , part of the straight line ABC , be in the

plane , and the part BC above it : and since the straight line AB is in the plane , it

can ...

I.

**THEOR**. ONE part of a straight line cannot be in a plane See N. and anotherpart above it . If it be possible , let AB , part of the straight line ABC , be in the

plane , and the part BC above it : and since the straight line AB is in the plane , it

can ...

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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 |

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

### 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.