## 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 5

Side 20

Let ABC be any triangle ; any two of A its angles together are less than two right

angles . Produce BC to D ; and because ACD is the exterior angle of the

...

Let ABC be any triangle ; any two of A its angles together are less than two right

angles . Produce BC to D ; and because ACD is the exterior angle of the

**triangle****ABC**, ACD is greater ( 16. 1. ) than the interior and opposite**angle ABC**; to each...

Side 319

c ܠ Let the sides AB , BC about the acute

has a right angle at A , have a given ratio to one another ; the

given in species . Take a straight line DE given in position and magnitude ; and ...

c ܠ Let the sides AB , BC about the acute

**angle ABC**of the**triangle ABC**, whichhas a right angle at A , have a given ratio to one another ; the

**triangle ABC**isgiven in species . Take a straight line DE given in position and magnitude ; and ...

Side 320

F the side AC ; take a straight line DE given in position and magnitude , and

make the angle DEF equal to the given

dat . ) in position ; and because the ratio of BA to AC is given , as BA to AC , so

make ...

F the side AC ; take a straight line DE given in position and magnitude , and

make the angle DEF equal to the given

**angle ABC**; therefore EF is given ( 32.dat . ) in position ; and because the ratio of BA to AC is given , as BA to AC , so

make ...

Side 387

The difference of an angle from a right angle is called the complement of that

angle . Thus , if BH be drawn perpendicular to AB , the angle CBH will be the

complement of the

which ...

The difference of an angle from a right angle is called the complement of that

angle . Thus , if BH be drawn perpendicular to AB , the angle CBH will be the

complement of the

**angle ABC**, or of CBF . IX . Let HK be the tangent , CL or DB ,which ...

Side 404

Let ABC be a spherical triangle , having a right angle at A ; the co - sine of the

hypothenuse BC will be to the radius , as the co - tangent of the

tangent of the

it ...

Let ABC be a spherical triangle , having a right angle at A ; the co - sine of the

hypothenuse BC will be to the radius , as the co - tangent of the

**angle ABC**to thetangent of the

**angle ACB**. Describe the circle DE , of which B is the pole , and letit ...

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The Elements of Euclid, Viz; The First Six Books: Together With the Eleventh ... Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2017 |

### 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.