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 |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 18.
Σελίδα 100
... arch BC to a quadrant , the confequents quadrupled ; then BAC is to four right angles as BC is to the whole ... arch BC to the whole circumference BCF ; therefore the arches IL , BC , are fimilar . COR . III . Two femidiameters AB , AC ...
... arch BC to a quadrant , the confequents quadrupled ; then BAC is to four right angles as BC is to the whole ... arch BC to the whole circumference BCF ; therefore the arches IL , BC , are fimilar . COR . III . Two femidiameters AB , AC ...
Σελίδα 145
... arch Book XII than a line equal to the tangent GL , then the right lines BK , KL , LM , ME , will each be lefs than the tangent GL ; and produce the lines joining the points K , A , o N ; and from the point A raife . AX perpendicular to ...
... arch Book XII than a line equal to the tangent GL , then the right lines BK , KL , LM , ME , will each be lefs than the tangent GL ; and produce the lines joining the points K , A , o N ; and from the point A raife . AX perpendicular to ...
Σελίδα 148
... arch from a quadrant or go degrees , is called the complement of that arch . III . A chord or fubtenfe , is a right line drawn from one part of an arch to another . IV . The IV . • The right fine , or fine of THE ...
... arch from a quadrant or go degrees , is called the complement of that arch . III . A chord or fubtenfe , is a right line drawn from one part of an arch to another . IV . The IV . • The right fine , or fine of THE ...
Σελίδα 149
... arch , is a right line drawn from the vertex of an arch perpendicular to the diameter of the circle , and is equal to half the chord of double that arch a If the arch DB , ( fig . for the def . ) is an arch of 30 deg . DE is the fine of ...
... arch , is a right line drawn from the vertex of an arch perpendicular to the diameter of the circle , and is equal to half the chord of double that arch a If the arch DB , ( fig . for the def . ) is an arch of 30 deg . DE is the fine of ...
Σελίδα 150
... arch DB be a very small arch , the fine and tangent are nearly to one another in the ratio of equa- lity . II . Because the chord of any arch , and its supplement to a circle , is the fame , so the fine , tangent , or fecant , of any ...
... arch DB be a very small arch , the fine and tangent are nearly to one another in the ratio of equa- lity . II . Because the chord of any arch , and its supplement to a circle , is the fame , so the fine , tangent , or fecant , of any ...
Άλλες εκδόσεις - Προβολή όλων
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 |
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 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.