## The Elements of Euclid: The Errors by which Theon, Or Others, Have Long 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 |

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Side 10

... of which the parts AB , AC are equal ; the remainder BF is equal * to the

remainder CG : and FC was

, FC are equal to the two CG , GB , each to each ; and the angle BFC was

to be ...

... of which the parts AB , AC are equal ; the remainder BF is equal * to the

remainder CG : and FC was

**proved**to be equal to GB ; therefore the two sides BF, FC are equal to the two CG , GB , each to each ; and the angle BFC was

**proved**to be ...

Side 155

Q. E. D. Cor . 1. In like manner it may be

or of any number of sides , are one to another in the duplicate ratio of their

homologous sides : and it has already been

Q. E. D. Cor . 1. In like manner it may be

**proved**that similar four - sided figures ,or of any number of sides , are one to another in the duplicate ratio of their

homologous sides : and it has already been

**proved**+ in triangles : † 19. Side 176

... and AF to FB , the two sides FA , AD are equal to the two FB , BC , each to each

; and the base DF was

equal * to the angle FBC : again , it was

...

... and AF to FB , the two sides FA , AD are equal to the two FB , BC , each to each

; and the base DF was

**proved**equal to the base FC ; therefore the angle FAD isequal * to the angle FBC : again , it was

**proved**that GA is equal to BH , and also...

Side 192

In the same manner it may be

MXN , and the angle GHK greater than MN the angle NXL : therefore the three

angles ABC , DEF , GHK are greater | 2 Cor.15 . than the three angles LXM , MXN

...

In the same manner it may be

**proved**that the angle DEF is greater than the angleMXN , and the angle GHK greater than MN the angle NXL : therefore the three

angles ABC , DEF , GHK are greater | 2 Cor.15 . than the three angles LXM , MXN

...

Side 288

there must be some equimultiples of B and A , and some multiple of C , such that

the multiple of B is greater than the multiple of C , but the multiple of A is not

greater than it : and it ought to have been

the ...

there must be some equimultiples of B and A , and some multiple of C , such that

the multiple of B is greater than the multiple of C , but the multiple of A is not

greater than it : and it ought to have been

**proved**, that this can never happen ifthe ...

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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ... Robert Simson Uten tilgangsbegrensning - 1775 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1762 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1781 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid excess figure fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition proved pyramid radius reason rectangle rectilineal figure remaining right angles segment shewn sides similar sine solid sphere square square of AC taken THEOR third triangle ABC wherefore whole

### Populære avsnitt

Side 141 - 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 40 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...

Side 26 - If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another, and the exterior angle equal to the interior and opposite upon the same side, and also the two interior angles upon the same side together equal to two right angles.

Side 46 - If 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 28 - Cor. angles; that is * together with four right angles. There1s, 1. fore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 21 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.

Side 12 - IF two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise their bases equal; the angle. which is contained by the two sides...

Side 169 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.

Side 5 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3. And that a circle may be described from any centre, at any distance from that centre.

Side 97 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.