## The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; 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 |

### Inni boken

Side 154

Let the

altitude , viz . the perpendicular drawn from ... BC is to the base CD , so is the

CF.

Let the

**triangles ABC**, ACD , and the parallelograms EC , CF , have the samealtitude , viz . the perpendicular drawn from ... BC is to the base CD , so is the

**triangle ABC**to the triangle ACD , and the parallelogram EC to the parallelogramCF.

Side 424

If a triangle have a given obtuse angle ; the excess of the square of the side

which subtends the obtuse angle , above the squares of the sides which contain

it , shall have a given ratio to the triangle . Let the

obtuse ...

If a triangle have a given obtuse angle ; the excess of the square of the side

which subtends the obtuse angle , above the squares of the sides which contain

it , shall have a given ratio to the triangle . Let the

**triangle ABC**have a givenobtuse ...

Side 425

quadruple of BD is to DA , that is , as quadruple of FH to HE , so is twice the

rectangle DB , BC to the

given ...

**triangle ABC**; therefore , ex æquali , as twice BD is to the half of DA , that is , asquadruple of BD is to DA , that is , as quadruple of FH to HE , so is twice the

rectangle DB , BC to the

**triangle ABC**. PROP . LXXV . 65 . Ir a triangle have agiven ...

Side 430

If a triangle have one angle given , and if the ratio of the rectangle of the sides

which contain the given angle to the square of the third side be given , the

triangle is given in species . Let the

let the ...

If a triangle have one angle given , and if the ratio of the rectangle of the sides

which contain the given angle to the square of the third side be given , the

triangle is given in species . Let the

**triangle ABC**have the given angle BAC , andlet the ...

Side 431

similar to OPQ : because , as has been shown , the ratio of AD to BC is the same

with the ratio of ( HF to FL , that is , by the construction , with the ratio of ) OR to

PQ ; and the angle BAC is equal to the angle POQ ; therefore the

...

similar to OPQ : because , as has been shown , the ratio of AD to BC is the same

with the ratio of ( HF to FL , that is , by the construction , with the ratio of ) OR to

PQ ; and the angle BAC is equal to the angle POQ ; therefore the

**triangle ABC**is...

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The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2015 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2016 |

The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Ingen forhåndsvisning tilgjengelig - 2018 |

### Vanlige uttrykk og setninger

added altitude angle ABC angle BAC base centre circle circle ABCD circumference common cone 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 greater Greek half join less likewise magnitude 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 9 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 81 - The angles in the same segment of a circle are equal to one another.

Side 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Side 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Side 49 - 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 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Side 155 - 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 22 - ANY two angles of a triangle are together less than two right angles.

Side 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.

Side 24 - Any two sides of a triangle are together greater than the third side.