## 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, to this Second Edition is Added 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 5

Side 233

R R R D | V o -— % / H A E C N tude; and that the solid DC is equal 8 to the solid

DZ, being upon the same base X R, and of the same

BT is equal to the solid DZ. but the bases are reciprocally proportional to the ...

R R R D | V o -— % / H A E C N tude; and that the solid DC is equal 8 to the solid

DZ, being upon the same base X R, and of the same

**altitude**; therefore the solidBT is equal to the solid DZ. but the bases are reciprocally proportional to the ...

Side 234

Bookxi. solid CD to the

parallelepipeds AB, CD are reciprocally proportional to their

the bases of the solids AB, CD be reciprocally proportional to their

Bookxi. solid CD to the

**altitude**of the solid AB; that is, the bases of the v_^^J solidparallelepipeds AB, CD are reciprocally proportional to their

**altitudes**. Next, Letthe bases of the solids AB, CD be reciprocally proportional to their

**altitudes**, viz. Side 261

BGML is the same with the

the base ABC to the base DEF, so is the

the

BGML is the same with the

**altitude**of the pyramid ABCC. there-Book xii. fore, asthe base ABC to the base DEF, so is the

**altitude**of the U-N-J pyramid DEFH tothe

**altitude**of the pyramid ABCG. wherefore the bases and**altitudes**of the ... Side 274

T H E O R. TH E bases and

reciprocally proportional; and if the bases and ... EC are reciprocally proportional;

that is, as the base ABCD to the base TFGH, so is the

KL.

T H E O R. TH E bases and

**altitudes**of equal cones and cylinders, arereciprocally proportional; and if the bases and ... EC are reciprocally proportional;

that is, as the base ABCD to the base TFGH, so is the

**altitude**MN to the**altitude**KL.

Side 275

But let the bases and

proportional, viz. the base ABCD to the base EFGH, as the

be equal to ...

But let the bases and

**altitudes**of the cylinders AX, EO, be reciprocallyproportional, viz. the base ABCD to the base EFGH, as the

**altitude**MN to the**altitudé**KL. the cylinder AX is equal to the cylinder EO. - - First, let the base ABCDbe equal to ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ... Robert Simson Uten tilgangsbegrensning - 1775 |

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... Robert Simson Uten tilgangsbegrensning - 1827 |

The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... Robert Simson Uten tilgangsbegrensning - 1781 |

### Vanlige uttrykk og setninger

added alſo altitude angle ABC angle BAC baſe BC is given becauſe Book caſe circle circle ABCD circumference common cone contained cylinder Definition demonſtrated deſcribed diameter divided double draw drawn equal equal angles equiangular equimultiples exceſs figure firſt fore four fourth given angle given in poſition given in ſpecies given magnitude given ratio given ſtraight line greater Greek half join leſs likewiſe manner meet muſt oppoſite P R O parallel parallelogram perpendicular plane produced Prop proportionals Propoſition pyramid reëtangle remaining right angles ſaid ſame ſame multiple ſecond ſegment ſhall ſhewn ſides ſimilar ſolid ſolid angle ſome ſquare ſquare of BC T H E O taken theſe third thro triangle ABC wherefore whole

### Populære avsnitt

Side 5 - Let it be granted that a straight line may be drawn from any one point to any other point.

Side 163 - 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 48 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.

Side 73 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle; and no straight line can be drawn from the extremity between that straight line and the circumference, so as not to cut the circle...

Side 105 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...

Side 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.

Side 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.

Side 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.

Side 47 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.

Side 37 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.