## 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 |

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Resultat 1-5 av 13

Side 16

DB and the straight line AB is divided into two equal parts in the point D. Which

was to be done . D B PROP . XI . PROB . To draw a straight line at right angles to

a

DB and the straight line AB is divided into two equal parts in the point D. Which

was to be done . D B PROP . XI . PROB . To draw a straight line at right angles to

a

**given straight line**, from a given point in the same . Let AB be a given straight ... Side 36

Then , because the

AHF , HFE are together equal ( 29. 1. ) ... To describe a parallelogram equal to a

Then , because the

**straight line**HF falls upon the parallels AH , EF , the anglesAHF , HFE are together equal ( 29. 1. ) ... To describe a parallelogram equal to a

**given**retilineal figure , and having an angle equal to a**given**rectilineal angle . Side 89

1 Let ABCDE be the

inscribe a circle in the pentagon ABCDE . Bisect ( 9. 1. ) the angles BCD , CDE by

the

1 Let ABCDE be the

**given**equilateral and equiangular pentagon : it is required toinscribe a circle in the pentagon ABCDE . Bisect ( 9. 1. ) the angles BCD , CDE by

the

**straight lines**CF , DF , and from the point F , in which they meet , draw the ... Side 181

... each , and situated in the same order , the solid angles are equal ( B. 11. )

each to each . Therefore the solid AL is similar ( 11. def . 11. ) to the solid CD .

Wherefore from a

described ...

... each , and situated in the same order , the solid angles are equal ( B. 11. )

each to each . Therefore the solid AL is similar ( 11. def . 11. ) to the solid CD .

Wherefore from a

**given straight line**AB , a solid parallelopiped AL has beendescribed ...

Side 249

... it is demonstrated indirectly , that the circle touches a

the 17th , 33d , and 37th propositions of ... where mention is made of a

angle , though there neither is , nor can be any thing in the proposition relating to

a ...

... it is demonstrated indirectly , that the circle touches a

**straight line**: whereas inthe 17th , 33d , and 37th propositions of ... where mention is made of a

**given**angle , though there neither is , nor can be any thing in the proposition relating to

a ...

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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.