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 10,000, and Tables of Sines, Tangents, and Secants, Natural and Artificialauthor, and sold, 1776 - 264 páginas |
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Página 102
... cone is a folid figure defcribed by a right angled triangle revolving about one of the fides , containing the right angle , remaining fixed . If the fixed right line be ... cone ; if lefs , an obtufe angled cone ; cone ; 102 ELEMENTS THE.
... cone is a folid figure defcribed by a right angled triangle revolving about one of the fides , containing the right angle , remaining fixed . If the fixed right line be ... cone ; if lefs , an obtufe angled cone ; cone ; 102 ELEMENTS THE.
Página 103
... cone ; if lefs , an obtufe angled cone ; and if greater , an a- Book XI . cute angled cone . XIX , The axis of a cone is that fixed right line about which the tri- angle is moved . XX . The base of a cone is the circle defcribed by the ...
... cone ; if lefs , an obtufe angled cone ; and if greater , an a- Book XI . cute angled cone . XIX , The axis of a cone is that fixed right line about which the tri- angle is moved . XX . The base of a cone is the circle defcribed by the ...
Página 138
... cone and cylinder , having the fame base , viz . the circle ABCD , and their altitudes equal , then the cone is one third of the cylinder ; that is , the cylinder is triple the cone . If not , it will be either greater or lefs than ...
... cone and cylinder , having the fame base , viz . the circle ABCD , and their altitudes equal , then the cone is one third of the cylinder ; that is , the cylinder is triple the cone . If not , it will be either greater or lefs than ...
Página 139
... cone , is greater than the cone whofe bafe is the circle ABCD ; and likewise less , as contained in it ; which cannot be ; therefore the cylinder is not lefs than triple the cone . Therefore , fince nei- ther greater nor lefs , it must ...
... cone , is greater than the cone whofe bafe is the circle ABCD ; and likewise less , as contained in it ; which cannot be ; therefore the cylinder is not lefs than triple the cone . Therefore , fince nei- ther greater nor lefs , it must ...
Página 140
... cone AL is to the folid X ; but the pyramid is greater than the folid X , and the cone AL graeater than the pyramid in it ; therefore , likewife the cone EN is greater than the pyramid in it ; but the pyramid in the cone EN is greater ...
... cone AL is to the folid X ; but the pyramid is greater than the folid X , and the cone AL graeater than the pyramid in it ; therefore , likewife the cone EN is greater than the pyramid in it ; but the pyramid in the cone EN is greater ...
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The Elements of Euclid: In Which the Propositions Are Demonstrated in a New ... Euclid Sin vista previa disponible - 2015 |
Términos y frases comunes
ABCM angle ABC angle BAC arch bafe bafe BC baſe becauſe bifected 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 reaſon fecond fegment femicircle fhall fides fimilar folid angle folid parallelopipedons fome fore fphere fquare of AC fubtending given right line greater infcribed join lefs leſs likewife magnitudes parallel parallelogram perpendicular plain paffing polygon polyhedron prifms PROP pyramid rectangle right angles right line AB right lined figure Secant Sine Tang tangent thefe THEOR theſe triangle ABC triplicate ratio Wherefore whofe bafe whoſe
Pasajes populares
Página 80 - 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.
Página 72 - F, equal to them in number, be taken two and two in the fame ratio, and if their analogy be perturbate, 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.
Página 91 - BAC was proved to be equal to ACD : Therefore the whole angle ACE is equal to the two angles ABC, BAC...
Página x - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles, these straight lines being continually produced, shall at length meet upon that side on which are the angles which are less than two right angles.
Página 54 - Let ABC be the given circle, and D the given straight line, not greater than the diameter of the circle. It is required to place in the circle ABC a straight line equal to D.
Página 9 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Página 13 - 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.
Página 69 - 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...
Página 91 - 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.
Página 80 - ... 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.