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 - Geometry - 264 pages |
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Results 1-5 of 40
Page viii
... proved from prop . 4. in very few words , and have not used more freedom than is done in the demonftration as it now stands . The fecond part , viz . the angles below the bafe , I have left out till the 13th is pro- ved , from which it ...
... proved from prop . 4. in very few words , and have not used more freedom than is done in the demonftration as it now stands . The fecond part , viz . the angles below the bafe , I have left out till the 13th is pro- ved , from which it ...
Page x
... prove the falfity of def . 10. Book XI . will appear from the following obfervations : He has proved that the triangles EAB , EBC , ECA , contain- ing the one folid , are equal and fimilar to the three triangles FAB , FBC , FCA ...
... prove the falfity of def . 10. Book XI . will appear from the following obfervations : He has proved that the triangles EAB , EBC , ECA , contain- ing the one folid , are equal and fimilar to the three triangles FAB , FBC , FCA ...
Page xi
... proved not univerfally true , he presents us with prop . A , B , C , after prop . 23. Book XI . to fupply its defect ... proved . The fame objection might be made with equal propriety to feveral others ; for example , why not prove the ...
... proved not univerfally true , he presents us with prop . A , B , C , after prop . 23. Book XI . to fupply its defect ... proved . The fame objection might be made with equal propriety to feveral others ; for example , why not prove the ...
Page xii
... is in the fame book with the propofition to be proved , the book is not named , but only the number of the propofition , but , if in other book , both are named . any THE ELEMENT S OF EU CLI D. BOOK I. DEFINITIONS Xii PREFACE .
... is in the fame book with the propofition to be proved , the book is not named , but only the number of the propofition , but , if in other book , both are named . any THE ELEMENT S OF EU CLI D. BOOK I. DEFINITIONS Xii PREFACE .
Page 5
... proved equal to AB , and BC to AB ; on 15 . therefore BC is equal to AC d . Therefore the three fides AB , BC , CA , are equal to one another : Therefore , upon the given right line AB , there is described an equilateral triangle ABC ...
... proved equal to AB , and BC to AB ; on 15 . therefore BC is equal to AC d . Therefore the three fides AB , BC , CA , are equal to one another : Therefore , upon the given right line AB , there is described an equilateral triangle ABC ...
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Common terms and phrases
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
Popular passages
Page 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...
Page 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.
Page 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.
Page 99 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Page 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.
Page 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...
Page 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.
Page 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.
Page 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...
Page 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.