Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)William Somerville Orr W.S. Orr and Company, 1854 - Science |
From inside the book
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Page 45
... centre of the circle . And any line drawn from the centre to the circumference is called a radius of the circle . XIV . A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference ...
... centre of the circle . And any line drawn from the centre to the circumference is called a radius of the circle . XIV . A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference ...
Page 47
... centre , at any distance from that centre . AXIOMS . I. Things which are equal to the same thing are equal to one another . II . If equals be added to equals , the wholes will be equal . III . If equals be taken from equals , the ...
... centre , at any distance from that centre . AXIOMS . I. Things which are equal to the same thing are equal to one another . II . If equals be added to equals , the wholes will be equal . III . If equals be taken from equals , the ...
Page 48
... centre A , and radius AB , describe the circle BCD ; * and with centre B , and the same radius , BA , describe the circle ACE . From C , the point in which the circles cut each other , draw CA , CB , * the triangle ABC shall * Post , 1 ...
... centre A , and radius AB , describe the circle BCD ; * and with centre B , and the same radius , BA , describe the circle ACE . From C , the point in which the circles cut each other , draw CA , CB , * the triangle ABC shall * Post , 1 ...
Page 49
... centre , and DG as radius , describe the circle G K L , and produce DA to meet it in * Post .. L ; * AL shall be equal to B C. Because B is the centre of the circle CGH , BC = + Def . 12. BG . † DG . Because D is the centre of the ...
... centre , and DG as radius , describe the circle G K L , and produce DA to meet it in * Post .. L ; * AL shall be equal to B C. Because B is the centre of the circle CGH , BC = + Def . 12. BG . † DG . Because D is the centre of the ...
Page 53
... centre C and radius C D * Post . 3. describe the circle E G F * meeting A B in F , G : bisect F G in H , + + Pr . 10. and join C , H. The straight line CH shall be perpendi- cular to A B. Draw CF , CG . Then because FH = * Const . GH ...
... centre C and radius C D * Post . 3. describe the circle E G F * meeting A B in F , G : bisect F G in H , + + Pr . 10. and join C , H. The straight line CH shall be perpendi- cular to A B. Draw CF , CG . Then because FH = * Const . GH ...
Common terms and phrases
ABCD Algebra arithmetic base Binomial Theorem bisect calculation called centre chord circumference coefficient common Completing the square contained cotan decimals denominator describe diameter divided dividend divisor draw ellipse equal angles equation equiangular equilateral Euclid EXAMPLES FOR EXERCISE expression exterior angle factors figure formula fraction frustum geometrical progression geometry given straight line greater h₂ Hence inscribed intersecting join latter less logarithm magnitudes manner measure multiplied operation parallel parallelogram perpendicular plane polygon prism Prop proportion proved Q. E. D. PROPOSITION quantity quotient radius ratio rectangle remainder result right angles rule sides sines solid angle sphere square root subtract suppose theorem third triangle ABC trigonometrical
Popular passages
Page 86 - If two triangles have two sides of the one equal to two sides of the...
Page 60 - 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...
Page 58 - ... equal angles in each ; then shall the other sides be equal each to each : and also the third angle of the one to the third angle of the other.
Page 45 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Page 190 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Page 47 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 151 - Equal parallelograms which have one angle of the one equal to one angle of the other, have their sides about the equal angles reciprocally proportional ; and parallelograms that have one angle of the one equal to one angle of the other, and their sides about the equal angles reciprocally proportional, are equal to one another.
Page 96 - angle in a segment' is the angle contained by two straight lines drawn from any point in the circumference of the segment, to the extremities of the straight line which is the base of the segment.
Page 46 - A rhombus, is that which has all its sides equal, but its angles are not right angles.
Page 66 - From this it is manifest how to a given straight line to apply a parallelogram, which shall have an angle equal to a given rectilineal angle, and shall be equal to a given rectilineal figure, viz.