The Elements of Euclid,: In which the Propositions are Demonstrated in a New and Shorter Manner Than in Former Translations, and the Arrangement of Many of Them Altered, to which are Annexed Plain and Spherical Trigonometry, Tables of Logarithms from 1 to 10000, and Tables of Sines, Tangents, and Secants, Both Natural and ArtificialJ. Murray, no. 32. Fleetstreet; and C. Elliot, Parliament-square, Edinburgh., 1776 - 264 σελίδες |
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Σελίδα 102
... pyramid is a solid figure , contained by more than two plains fet upon one plain , and meeting at one point in the vertex . XIII . A prism is a solid figure contained by plains , whereof the two opposite are equal , similar , and ...
... pyramid is a solid figure , contained by more than two plains fet upon one plain , and meeting at one point in the vertex . XIII . A prism is a solid figure contained by plains , whereof the two opposite are equal , similar , and ...
Σελίδα 132
... pyramid having a triangular base , may be divided into two pyramids , equal and fimilar to one another , having triangular bases , and fimilar to the whole pyramid ; and into two equal prisms ; which two prisms are greater than the half ...
... pyramid having a triangular base , may be divided into two pyramids , equal and fimilar to one another , having triangular bases , and fimilar to the whole pyramid ; and into two equal prisms ; which two prisms are greater than the half ...
Σελίδα 133
... pyramid , whose base is the triangle ABC , and Book XII vertex the point M , then the pyramid ABCM may be divided in- ~ to two pyramids , equal and fimilar to one another , having tri- angular bases , and similar to the whole ; and into ...
... pyramid , whose base is the triangle ABC , and Book XII vertex the point M , then the pyramid ABCM may be divided in- ~ to two pyramids , equal and fimilar to one another , having tri- angular bases , and similar to the whole ; and into ...
Σελίδα 134
... pyramid . а д . б . b 22. 6 . c 32. and 28. 11 . 3- PROP . IV . THEOR . TF there are two pyramids of the fame ... pyramid be divided in the same manner , and this be done continually ; then , as the base of the one pyramid is to ...
... pyramid . а д . б . b 22. 6 . c 32. and 28. 11 . 3- PROP . IV . THEOR . TF there are two pyramids of the fame ... pyramid be divided in the same manner , and this be done continually ; then , as the base of the one pyramid is to ...
Σελίδα 135
... pyramid ABCM to the two prisms in the pyramid DEFH . For the same reason , the prisms in the py- ramids HKLM , STYH , or any other pyramids made by any of the former divifions , are to each other as their bafes ; wherefore , all the ...
... pyramid ABCM to the two prisms in the pyramid DEFH . For the same reason , the prisms in the py- ramids HKLM , STYH , or any other pyramids made by any of the former divifions , are to each other as their bafes ; wherefore , all the ...
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The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCM angle ABC angle BAC arch baſe BC becauſe biſect Book XI circle ABCD circle EFGH circumference cofine common fection cone contained cylinder DEFH deſcribe diameter draw drawn equal angles equal to AC equiangular equilateral equimultiples fame altitude fame multiple fame plain fame proportion fame reaſon fides fimilar firſt folid angle fore fubtend given right line greater inſcribed join leſs Let ABC likewife magnitudes oppoſite parallel parallelogram perpendicular plain angles polygon priſm PROB PROP pyramid rectangle right angles right lined figure ſame Secant ſecond ſegment ſhall ſide Sine ſolid ſome ſphere ſquare ſquare of AC Tang tangent THEOR theſe triangle ABC triplicate ratio verſed Wherefore whoſe baſe
Δημοφιλή αποσπάσματα
Σελίδα 93 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG ; the...
Σελίδα 78 - ... viz. as A is to B, fo is E to F, and B to C as D to E ; and if the firft A be greater than the third C, then the fourth D will be greater than the fixth F ; if equal, equal ; and, if lefs, lefs.
Σελίδα 88 - 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 99 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Σελίδα 19 - From this it is manifest that if one angle of a triangle be equal to the other two it is a right angle, because the angle adjacent to it is equal to the same two ; (i.
Σελίδα 75 - Let AB be the fame multiple of C, that DE is of F : C is to F, as AB to DE. Becaufe AB is the fame multiple of C that DE is of F ; there are as many magnitudes in AB equal to C, as there are in DE equal...
Σελίδα 88 - ... reciprocally proportional, are equal to one another. Let AB, BC be equal parallelograms which have the angles at B equal, and let the sides DB, BE be placed in the same straight line ; wherefore also FB, BG are in one straight line (2.
Σελίδα 99 - BGC: for the same reason, whatever multiple the circumference EN is of the circumference EF, the same multiple is the angle EHN of the angle EHF: and if the circumference BL be equal to the circumference EN, the angle BGL is also equal to the angle EHN ; (in.
Σελίδα 106 - ... but BD, BE, which are in that plane, do each of them meet AB ; therefore each of the angles ABD, ABE is a right angle ; for the same reason, each of the angles CDB, CDE is a right angle: and because AB is equal to DE, and BD...
Σελίδα 73 - RATIOS that are the same to the same ratio, are the same to one another. Let A be to B as C is to D ; and as C to D, so let E be to F ; A is to B, as E to F.