Elements of Geometry: Containing the Principal Propositions in the First Six, and the Eleventh and Twelfth Books of EuclidJ. Johnson, 1789 - 272 σελίδες |
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Σελίδα vi
... demonstration ; the latter of which , in particular , it is prefumed , will be found confiderably improved , being here delivered in a more convenient form , and rendered as clear and explicit as the nature of the fub- ject would admit ...
... demonstration ; the latter of which , in particular , it is prefumed , will be found confiderably improved , being here delivered in a more convenient form , and rendered as clear and explicit as the nature of the fub- ject would admit ...
Σελίδα 252
... demonstration as much as any Prop . in the Elements ; and it is always obferved that learners , instead of giving that ready affent to it which an axiomatical principle requires , receive it with doubt and hefitation , and are fcarcely ...
... demonstration as much as any Prop . in the Elements ; and it is always obferved that learners , instead of giving that ready affent to it which an axiomatical principle requires , receive it with doubt and hefitation , and are fcarcely ...
Σελίδα 254
... demonstration of this propofition , has fhewn that the angles below the bafe are , alfo , equal to each other . But as this property is never referred to throughout the Elements , except in the demonftration of the 2d cafe of the 7th ...
... demonstration of this propofition , has fhewn that the angles below the bafe are , alfo , equal to each other . But as this property is never referred to throughout the Elements , except in the demonftration of the 2d cafe of the 7th ...
Σελίδα 256
... demonstration of this propofition , as it is given by EUCLID , is extremely defective ; for the whole defign of the problem is to fhew that of three right lines , under certain fpecified reftrictions , a triangle may be formed ; and as ...
... demonstration of this propofition , as it is given by EUCLID , is extremely defective ; for the whole defign of the problem is to fhew that of three right lines , under certain fpecified reftrictions , a triangle may be formed ; and as ...
Σελίδα 264
... demonstrations of these propofitions are confined to one cafe , which , though it does not include every poffi- ble pofition of the lines , will , it is conceived , be thought fufficiently general . EUCLID , in this inftance , is much ...
... demonstrations of these propofitions are confined to one cafe , which , though it does not include every poffi- ble pofition of the lines , will , it is conceived , be thought fufficiently general . EUCLID , in this inftance , is much ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Geometry: Containing the Principal Propositions in the First Six ... Euclid,John Bonnycastle Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD AC is equal alfo equal alſo be equal alſo be greater altitude angle ABC angle ACB angle BAC angle CAB angle DAF bafe baſe becauſe bifect cafe centre chord circle ABC circumference Conft defcribe demonftration diagonal diameter diſtance draw EFGH equiangular equimultiples EUCLID fame manner fame multiple fame plane fame ratio fecond fection fegment fhewn fide AB fide AC fimilar fince the angles folid fome fquares of AC ftand given circle given right line infcribed interfect join the points lefs leſs Let ABC magnitudes muſt oppofite angles outward angle parallelepipedons parallelogram perpendicular polygon prifm propofition proportional Q. E. D. PROP reafon rectangle of AB rectangle of AC remaining angle right angles SCHOLIUM ſhall ſpace ſquare tangent THEOREM theſe thofe thoſe triangle ABC twice the rectangle whence
Δημοφιλή αποσπάσματα
Σελίδα 166 - 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.
Σελίδα 73 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 215 - Lemma, if from the greater of two unequal magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there shall at length remain a magnitude less than the least of the proposed magnitudes.
Σελίδα 117 - In a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF. Draw the straight line GAH touching the circle in the point A (III. 17), and at the point A, in the straight line AH, make the angle HAG equal to the angle DEF (I.
Σελίδα 18 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. LET ab be the given straight line, which may be produced to any length both ways, and let c be a point without it. It is required to draw a straight line perpendicular to ab from the point c.
Σελίδα 249 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Σελίδα 102 - To bisect a given arc, that is, to divide it into two equal parts. Let ADB be the given arc : it is required to bisect it.
Σελίδα i - Handbook to the First London BA Examination. Lie (Jonas). SECOND SIGHT; OR, SKETCHES FROM NORDLAND. By JONAS LIE. Translated from the Norwegian. [/» preparation. Euclid. THE ENUNCIATIONS AND COROLLARIES of the Propositions in the First Six and the Eleventh and Twelfth Books of Euclid's Elements.
Σελίδα 5 - AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will be unequal.
Σελίδα 145 - F is greater than E; and if equal, equal; and if less, less. But F is any multiple whatever of C, and D and E are any equimultiples whatever of A and B; [Construction.