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 viii
... angles below the bafe , I have left out till the 13th is pro- ved , from which it eafily follows ; and likewife in proving the bafes equal in the 4th , I have changed the indirect proof , and given a direct one , by which it is both ...
... angles below the bafe , I have left out till the 13th is pro- ved , from which it eafily follows ; and likewife in proving the bafes equal in the 4th , I have changed the indirect proof , and given a direct one , by which it is both ...
Σελίδα xi
... equal and fimilar planes alike fituated , and having none " of their folid angles contained by more than three plane angles , are equal and fimilar to one another . " But this prop . C. will e- vidently appear infufficient to supply ...
... equal and fimilar planes alike fituated , and having none " of their folid angles contained by more than three plane angles , are equal and fimilar to one another . " But this prop . C. will e- vidently appear infufficient to supply ...
Σελίδα xii
... equal to fome folid as GA BC , either greater or less than EABC , which cannot be ; for the one would contain the other ; and if the folid angle is con- B G E D tained by more than three plane angles ... angles which are contained by ...
... equal to fome folid as GA BC , either greater or less than EABC , which cannot be ; for the one would contain the other ; and if the folid angle is con- B G E D tained by more than three plane angles ... angles which are contained by ...
Σελίδα 2
... equal . XVI . That point is called the center of the circle . XVII . The diameter of a circle is a right line drawn ... angles lefs than right ones . XXX . A XXX . A fquare is that which hath four equal THE ELEMENTS.
... equal . XVI . That point is called the center of the circle . XVII . The diameter of a circle is a right line drawn ... angles lefs than right ones . XXX . A XXX . A fquare is that which hath four equal THE ELEMENTS.
Σελίδα 3
... equal fides , and its angles all right ones . XXXI . An oblong , or rectangle , is longer than broad , its oppofite fides are equal , and its angles all right ones . XXXII . A rhombus , that which hath four equal fides , but not right ...
... equal fides , and its angles all right ones . XXXI . An oblong , or rectangle , is longer than broad , its oppofite fides are equal , and its angles all right ones . XXXII . A rhombus , that which hath four equal fides , but not right ...
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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.