## The Elements of Euclid: With Dissertations Intended to Assist and Encourage a Critical Examination of These Elements as the Most Effectual Means of Establishing a Juster Taste Upon Mathematical Subjects Than that which at Present PrevailsPrinted at the Clarendon Press, 1781 - 309 Seiten |

### Im Buch

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**should**think they know nothing but their bufinefs and therefore instead of explaining their author , endeavour to perfuade the world that they understand the fubject better than he himself did . But I do not write to the ftrength but to ... Seite 6

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**should**conjure up a prejudice which we might want art afterwards to lay . By the affistance of this triangular piece of wood , make two equal incli- nations ( or angles ) upon paper , taking care to make the lines une- qual , to prevent ... Seite 8

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**should**pretend that he had the notions orginally in this very general form to which I have been endeavouring to lead him ; I have only to say , unless they were acquired by an exami- nation of particulars , he will find his notions fit ... Seite 10

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**should**be infer- red from the other fcientifically ; but only that the definition ex- preffes the conception , derived from two lines , reduced into a more fimple form ; though indeed he himself reafons from the common notion as will ... Seite 12

... bugbear in the way of the reader ; only I was afraid left he might stumble upon it of himself , with fome hazard to his understanding , if he

... bugbear in the way of the reader ; only I was afraid left he might stumble upon it of himself , with fome hazard to his understanding , if he

**should**pursue the the metaphyfical analysis of it , until he had no 12 DISSERTATION I.### Andere Ausgaben - Alle anzeigen

The Elements of Euclid: With Dissertations Intended to Assist and Encourage ... James Williamson,James Euclid Keine Leseprobe verfügbar - 2016 |

### Häufige Begriffe und Wortgruppen

ABCD alfo alſo angle ABC angle BAC angle contained angle equal apply itſelf bafe baſe BC is equal Book certainly circle ABC circumference common notion confequences conft conftruction cut in halves demonftrated deſcribed diſtance drawn equal angles equiangular equilateral equimultiples Euclid exceed faid fame manner fame multiple fame parallels fame ratio fame reaſon fecond fegment fhall fides fimilar fince firſt fome fquare ftraight line BC fuch fuppofe fuppofition given rectilineal given ſtraight line Gnomon greater hath himſelf impoffible infcribed joined lefs leſs let the ftraight magnitudes moſt muſt neceffary parallelogram PROP propofition proportionals purpoſe reader reaſon rectangle contained rectilineal figure remaining angle remaining fides right angles ſame ſay ſhall ſhould ſome ſquare ſtraight line AB ſubject ſuch ſuppoſe taken theſe thoſe tiple triangle ABC underſtand uſe Wherefore becauſe

### Beliebte Passagen

Seite 3 - Let it be granted that a straight line may be drawn from any one point to any other point.

Seite 47 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...

Seite 68 - If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre, it shall cut it at right angles : and if it cut it at right angles, it shall bisect it.

Seite 45 - ABG ; (vi. 1.) therefore the triangle ABC has to the triangle ABG the duplicate ratio of that which BC has to EF: but the triangle ABG is equal to the triangle DEF; therefore also the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. Therefore similar triangles, &c.

Seite 15 - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.

Seite 86 - When you have proved that the three angles of every triangle are equal to two right angles...

Seite 88 - EA : and because AD is equal to DC, and DE common to the triangles ADE, CDE, the two sides AD, DE are equal to the two CD, DE, each to each ; and the angle ADE is equal to the angle CDE, for each of them is a right angle ; therefore the base AE is equal (4.

Seite 42 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means ; And if the rectangle contained by the extremes be equal to the rectangle contained by the means, the four straight lines are proportionals. Let the four straight lines, AB, CD, E, F, be proportionals, viz.

Seite 109 - Draw two diameters AC, BD of the circle ABCD, at right angles to one another; and through the points A, B. C, D, draw (17.

Seite 8 - GB is equal to E, and CK to F ; therefore AB is the same multiple of E, that KH is of F: But AB...