## 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 40

I. EVERY right angled parallelogram is said to be

straight lines which

any of the parallelograms about a diameter , together with the two complements

is E ...

I. EVERY right angled parallelogram is said to be

**contained**by any two of thestraight lines which

**contain**one of the right angles . II . In every parallelogram ,any of the parallelograms about a diameter , together with the two complements

is E ...

Side 41

is

DE , because DK , that is ( 34. 1. ) BG is equal to A ; and in like manner the ...

**contained**by GB , BC , and GB is equal to A ; and BK is**contained**by A , BD , for itis

**contained**by GB , BD , of which GB is equal to A ; and DL is**contained**by A ,DE , because DK , that is ( 34. 1. ) BG is equal to A ; and in like manner the ...

Side 86

... one of which cuts , and the other meets the circle , and that the rectangle AB , A

BC

is equal to the square of BD which meets it ; the straight line BD touches С ( 34.

... one of which cuts , and the other meets the circle , and that the rectangle AB , A

BC

**contained**by the whole of the cutting line , and the part of it without the circleis equal to the square of BD which meets it ; the straight line BD touches С ( 34.

Side 136

Q. E. D. PROP . XVI . THEOR . If four straight lines be proportionals , the rectangle

if the rectangle

Q. E. D. PROP . XVI . THEOR . If four straight lines be proportionals , the rectangle

**contained**by the extremes is equal to the rectangle**contained**by the means : andif the rectangle

**contained**by the extremes be equal to the rectangle**contained**... Side 137

IF three straight lines be proportionals , the rectangle

is equal to the square of the mean : and if the rectangle

extremes be equal to the square of the mean , the three straight lines are

proportionals .

IF three straight lines be proportionals , the rectangle

**contained**by the extremesis equal to the square of the mean : and if the rectangle

**contained**by theextremes be equal to the square of the mean , the three straight lines are

proportionals .

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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.