## 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 164

GH , DE . But if a straight line stands at right angles to each of two straight lines in

the ...

**perpendicular**to AF ; and consequently AF is**perpendicular**to GH , and AF is**perpendicular**to DE : therefore AF is**perpendicular**to each of the straight linesGH , DE . But if a straight line stands at right angles to each of two straight lines in

the ...

Side 168

IF two planes cutting one another be each of them

their common section shall be

planes AB , BC be each of them

...

IF two planes cutting one another be each of them

**perpendicular**to a third plane ;their common section shall be

**perpendicular**to the same plane . Let the twoplanes AB , BC be each of them

**perpendicular**to a third plane , and let BD be the...

Side 197

... one of the planes

on the common section of the planes . " * " Let the plane CD be

the plane AB , and let AD be their common section ; if any point E be taken in the

...

... one of the planes

**perpendicular**to the other plane , this straight line shall fallon the common section of the planes . " * " Let the plane CD be

**perpendicular**tothe plane AB , and let AD be their common section ; if any point E be taken in the

...

Side 345

Draw AD

wherefore the ratio of BD to AR is given : and the ratio of AR to BC is given , and

consequently ( 9. dat . ) the ratio of AD to BC is given ; and the triangle ABC is ...

Draw AD

**perpendicular**to BC ; therefore the triangle ARD is given in species ;wherefore the ratio of BD to AR is given : and the ratio of AR to BC is given , and

consequently ( 9. dat . ) the ratio of AD to BC is given ; and the triangle ABC is ...

Side 402

In any spherical triangle ABC , if the

fall within the triangle , the angles B and C at the base will be of the same

affection ; and if the

will be of ...

In any spherical triangle ABC , if the

**perpendicular**AD from A on the base BC ,fall within the triangle , the angles B and C at the base will be of the same

affection ; and if the

**perpendicular**fall without the triangle , the angles B and Cwill be of ...

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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.