A treatise on navigation, and nautical astronomy |
From inside the book
Results 1-5 of 22
Page viii
... squares read square . Theorem 54 , for B A C read BAD . for F read E. for P Qread B Q , and for : C reail C : . 10 , 33 , 9 , 36 , 11 , 39 , 44 , 9 , 13 , 48 , 19 , 50 , 11 , 50 , 19 , for B C read B E. 50 , for A C G read A G C. for ...
... squares read square . Theorem 54 , for B A C read BAD . for F read E. for P Qread B Q , and for : C reail C : . 10 , 33 , 9 , 36 , 11 , 39 , 44 , 9 , 13 , 48 , 19 , 50 , 11 , 50 , 19 , for B C read B E. 50 , for A C G read A G C. for ...
Page 31
... squares on equal lines are equal to each other . THEOREM XXXVIII . If A B C D be any parallelogram , and BD a diagonal of it ; and if EIF be drawn parallel to A B or C D , and G IH parallel to A D or BC , making the parallelograms HF ...
... squares on equal lines are equal to each other . THEOREM XXXVIII . If A B C D be any parallelogram , and BD a diagonal of it ; and if EIF be drawn parallel to A B or C D , and G IH parallel to A D or BC , making the parallelograms HF ...
Page 32
... squares of the two parts A F and F B , and twice the rectangle contained by those parts . A B2 , or A F + F B2 = A F2 + B F2 + 2 AF.FB. For let A C be the square on A B , and FI the square on F B , and produce F G and IG , till they ...
... squares of the two parts A F and F B , and twice the rectangle contained by those parts . A B2 , or A F + F B2 = A F2 + B F2 + 2 AF.FB. For let A C be the square on A B , and FI the square on F B , and produce F G and IG , till they ...
Page 33
... squares of A C and BC by twice the rectangle of AC and B C. A B2 + B C2 2 А В. В С. Or A C B C2 For let A B D E be the square on the difference A B , and A C F G the square on the line A C. Pro- duce ED to H ; also produce D B and HC ...
... squares of A C and BC by twice the rectangle of AC and B C. A B2 + B C2 2 А В. В С. Or A C B C2 For let A B D E be the square on the difference A B , and A C F G the square on the line A C. Pro- duce ED to H ; also produce D B and HC ...
Page 34
... squares A D and A F. But D I is a rectangle contained under DK the sum , and K I the difference of A B and A C. Hence the differ- ence of the squares of A B and A C is equal to the rectangle of their sum and difference . Or if A B be ...
... squares A D and A F. But D I is a rectangle contained under DK the sum , and K I the difference of A B and A C. Hence the differ- ence of the squares of A B and A C is equal to the rectangle of their sum and difference . Or if A B be ...
Other editions - View all
Common terms and phrases
angled spherical triangle Answer apparent altitude Atlantic Ocean bisected Cape celestial object centre chronometer circle column compass computed correction Cosec Cosine Cotang course and distance declination diff lat diff long Difference of Latitude difference of longitude Dist equal equator EXAMPLES FOR EXERCISE Given A B greater Greenwich Hence horizontal parallax Indian Archipelago Indian Ocean Island Latitude and Departure latitude and longitude logarithm longitude Lunar Distance meridian distance miles moon moon's Nautical Almanac noon observed opposite Pacific Ocean parallax parallel parallel sailing parallelogram perpendicular plane sailing polar distance pole quadrant radius rectangle rhumb line right angled spherical right ascension Secant semidiameter sides squares of A C subtract Suvers Suversed Sines Table Tang tangent Theo THEOREM triangle A B C true altitude true distance Vers
Popular passages
Page 18 - LET it be granted that a straight line may be drawn from any one point to any other point.
Page 17 - When equals are taken from unequals, the remainders are unequal. 6. Things which are double of the same thing, or equal things, are equal to each other.
Page 86 - III.), is a circle. If the plane pass through the centre, then, as every point in the surface of the sphere is equidistant from its centre, the section is a plane figure, every point of whose periphery is equidistant from a certain point within it, and the figure is therefore a circle. But if the plane do not pass through...
Page 26 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 114 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 63 - If from a point without a circle two straight lines be drawn, one of which...
Page 147 - Mathematical o>jgraphy.) the arc of the equator, intercepted between the first meridian...
Page 64 - If from any point without a circle straight lines be drawn touching it, the angle contained by the tangents is double the angle contained by the straight line joining the points of contact and the diameter drawn through one of them.
Page 139 - Given the vertical angle, the difference of the two sides containing it, and the difference of the segments of the base made by a perpendicular from the vertex ; construct the triangle.
Page 86 - ... half a right angle, as the tangent of half the sum of the angles, at the base of the triangle to the tangent of half their difference.