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 133
... ABCM is fimilar to HKLM ; but the pyramid AEHG is proved fimilar to HKLM , therefore fimilar to one ħ 21. 6 nother , and similar to ABCM . i Again , because BN is equal to NC , the parallelogram BG is double the triangle GNC ; therefore ...
... ABCM is fimilar to HKLM ; but the pyramid AEHG is proved fimilar to HKLM , therefore fimilar to one ħ 21. 6 nother , and similar to ABCM . i Again , because BN is equal to NC , the parallelogram BG is double the triangle GNC ; therefore ...
Σελίδα 134
... ABCM to all the prifms in the pyramid DEFH , being equal in number . For , let the pyramid DEFH be constructed fimilar to the py- ramid ABCM ; then , all the triangles described in the base ABC being fimilar to the whole , and to one ...
... ABCM to all the prifms in the pyramid DEFH , being equal in number . For , let the pyramid DEFH be constructed fimilar to the py- ramid ABCM ; then , all the triangles described in the base ABC being fimilar to the whole , and to one ...
Σελίδα 135
... ABCM to the two prisms in the pyramid DEFH . For the fame 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 prisms in ...
... ABCM to the two prisms in the pyramid DEFH . For the fame 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 prisms in ...
Σελίδα 136
... ABCM is to the pyramid ACDM as the bate ABC is to the bafe ACD ; and ACDM is to ADEM as ACD is to AED ; therefore the whole ABCDEM is to ABCM as ABCDE to ABC d . For the fame reason , as FGHKLN is to FGHKL as FGHN is to FGH ; if ABCDE ...
... ABCM is to the pyramid ACDM as the bate ABC is to the bafe ACD ; and ACDM is to ADEM as ACD is to AED ; therefore the whole ABCDEM is to ABCM as ABCDE to ABC d . For the fame reason , as FGHKLN is to FGHKL as FGHN is to FGH ; if ABCDE ...
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The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2022 |
The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2022 |
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCM angle ABC angle BAC arch bafe baſe becauſe bifect Book XI circle ABCD circle EFGH circumference cofine common fection cone contained cylinder defcribe DEFH diameter draw drawn equal angles equal to AC equiangular equilateral equimultiples fame altitude fame multiple fame plain fame proportion fame reafon fecond fegment femicircle fides fimilar folid angle fome fore fquare of AC fubtending given right line greater infcribed join lefs leſs Let ABC magnitudes oppofite parallel parallelogram perpendicular plain angles plain paffing polygon prifms Prop pyramid rectangle right angles right line AB right lined figure Secant Sine ſphere ſquare Tang tangent thefe THEOR theſe triangle ABC triplicate ratio Wherefore whofe ΙΟ
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.