## 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 29

Side 25

to

also the third angle of the one to the third angle of the other . Let ABC , DEF be

two triangles which have the angles ABC , BCA

viz ...

to

**equal**angles in each ; then shall the other sides be**equal**, each to each ; andalso the third angle of the one to the third angle of the other . Let ABC , DEF be

two triangles which have the angles ABC , BCA

**equal**to the angles DEF , EFD ,viz ...

Side 36

Then , because the straight line HF falls upon the parallels AH , EF , the angles

AHF , HFE are together

BHF , HFE are less than two right angles : but straight lines which with another ...

Then , because the straight line HF falls upon the parallels AH , EF , the angles

AHF , HFE are together

**equal**( 29. 1. ) to two right angles : wherefore the anglesBHF , HFE are less than two right angles : but straight lines which with another ...

Side 71

If the angle BGC be

BAC is also

let BGC be the greater : and at the point G , in the straight line BG , make ( 23.

If the angle BGC be

**equal**to the angle EHF , it is manifest ( 20. 3. ) that the angleBAC is also

**equal**to EDF : but , if not , one of them is A D G a B F С K the greater ;let BGC be the greater : and at the point G , in the straight line BG , make ( 23.

Side 72

circumferences , when they are at the centres ; therefore the circumference BGC

is

whole EDF ; the remaining part therefore of the circumference , viz . BAC , is

circumferences , when they are at the centres ; therefore the circumference BGC

is

**equal**to the circumference EHF . But the whole circle ABC is**equal**to thewhole EDF ; the remaining part therefore of the circumference , viz . BAC , is

**equal**to ... Side 86

Join AC , BD cutting one another in E ; and because DA is

common to the triangles DAC , BAC , the two sides DA , AC are

BA , AC ; and А the base DC is

DAC ...

Join AC , BD cutting one another in E ; and because DA is

**equal**to AB , and ACcommon to the triangles DAC , BAC , the two sides DA , AC are

**equal**to the twoBA , AC ; and А the base DC is

**equal**to the base BC ; whereD fore the angleDAC ...

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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.