## 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 twelfth |

### Inni boken

Resultat 1-5 av 18

Side 25

to the base DF , and the triangle GBC to the triangle DEF , and the other angles to

the other angles , each to each , to which the equal sides are

the angle GCB is equal to the angle DFE ; but DFE is , by the hypothesis ...

to the base DF , and the triangle GBC to the triangle DEF , and the other angles to

the other angles , each to each , to which the equal sides are

**opposite**; thereforethe angle GCB is equal to the angle DFE ; but DFE is , by the hypothesis ...

Side 36

to two right angles : therefore also KHG , GHM are equal to two right angles ; and

because at the point H in the straight B CK H M Jine GH , the two straight lines

KH , HM , upon the

to two right angles : therefore also KHG , GHM are equal to two right angles ; and

because at the point H in the straight B CK H M Jine GH , the two straight lines

KH , HM , upon the

**opposite**sides of it , make the adjacent angles equal to two ... Side 89

1 ) to the base FD , and the other angles to the other angles , to which the equal

sides are

because the angle CDE is double of CDF , and that CDE is equal to CBA , and

CDF ...

1 ) to the base FD , and the other angles to the other angles , to which the equal

sides are

**opposite**; therefore the angle CBF is equal to the angle CDF : andbecause the angle CDE is double of CDF , and that CDE is equal to CBA , and

CDF ...

Side 154

The rectangle contained by the diagonals of a quadrilateral inscribed in a circle ,

is equal to both the rectangles contained by its

any quadrilateral inscribed in a circle , and join AC , BD ; the rectangle contained

...

The rectangle contained by the diagonals of a quadrilateral inscribed in a circle ,

is equal to both the rectangles contained by its

**opposite**sides . * Let ABCR beany quadrilateral inscribed in a circle , and join AC , BD ; the rectangle contained

...

Side 177

If a solid be contained by six planes , two and two of which are parallel ; the

contained by the parallel planes AC , GF ; BG , CE ; FB , AE : its

are ...

If a solid be contained by six planes , two and two of which are parallel ; the

**opposite**planes are similar and equal parallelograms . * Let the solid CDGH becontained by the parallel planes AC , GF ; BG , CE ; FB , AE : its

**opposite**planesare ...

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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid,Robert Simson Uten tilgangsbegrensning - 1825 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid Uten tilgangsbegrensning - 1892 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples Euclid excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line gles greater Greek half join less likewise manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition pyramid Q. E. D. PROP radius reason rectangle rectangle contained rectilineal figure 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 45 - Ir 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 41 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Side 54 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.

Side 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.

Side 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.

Side 8 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 256 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Side 129 - 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 23 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...

Side 20 - ANY two angles of a triangle are together less than two right angles.