## The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 sider |

### Inni boken

Resultat 1-5 av 68

Side 11

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**diameter**of a circle is a ftraight line drawn through the see N. centre , and terminated both ways by the circumference . XVIII . A femicircle is the figure contained by a**diameter**and the part of the circumference cut off by the**diameter**... Side 39

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**diameter**is the ftraight line joining two of its oppofite angles . Let ACDB be a parallelogram , of which BC is a**diameter**; the oppofite fides and angles of the figure are equal to one an other ; and the**diameter**BC bifects it . C B D ... Side 40

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**diameter**BC divides the parallelogram ACDB into two equal parts . Q. E. D. C 4. I. See N. See the 2d PRO P. XXXV . THEOR . ARALLELOGRAMS upon the fame bafe and between the fame parallels , are equal to one another , PAR Let the ... Side 42

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**diameter**AB bifects c it ; and the triangle DBC is the half of the parallelo- gram DBCF , because the**diameter**DC bifects it : But the d 7. Ax . halves of equal things are equal d ; therefore the triangle ABC is equal to the triangle ... Side 44

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**diameter**AC di- vides it into two equal parts ; where- fore ABCD is alto double of the tri- A B DE angle EBC . Therefore , if a parallelogram , & c . Q. E. D. PROP . XLII . PROB . Τ To defcribe a parallelogram that fhall be equal to a ...### Andre utgaver - Vis alle

The First Six Books: Together with the Eleventh and Twelfth Euclid Ingen forhåndsvisning tilgjengelig - 2016 |

### Vanlige uttrykk og setninger

alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe centre circle ABCD circumference cone confequently cylinder defcribed demonftrated drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fide BC fides fimilar firft firſt folid angle fome fore fphere fquare of AC ftraight line AB ftraight line BC given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs likewife oppofite parallel parallelepipeds parallelogram perpendicular plane angles prifms PROP propofition pyramid ratio of BC rectangle contained rectilineal figure right angles ſquare thefe THEOR theſe triangle ABC wherefore

### Populære avsnitt

Side 472 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.

Side 170 - 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 81 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...

Side 105 - DEF are likewise equal (13. i.) to two right angles ; therefore the angles AKB, AMB are equal to the angles DEG, DEF, of which AKB is equal to DEG ; wherefore the remaining angle AMB is equal to the remaining angle DEF.

Side 167 - AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off.

Side 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.

Side 62 - 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 112 - To describe an equilateral and equiangular pentagon about a given circle. • Let ABCDE be the given circle; it is required to describe an equilateral and equiangular pentagon about the circle ABCDE. Let the angles of a pentagon, inscribed in the circle...

Side 200 - 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 38 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.