Elements of Geometry and Conic Sections |
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Σελίδα 7
The Proportions of Figures . . . BOOK V . Problems relating to the preceding
Books . BOOK VI . Regular Polygons , and the Area of the Circle . . . . . . 83 . . . . . . .
. 11 % SOLID GEOMETRY . BOOK VIL Planes and Solid Angles . . . . . . BOOK VIII
.
The Proportions of Figures . . . BOOK V . Problems relating to the preceding
Books . BOOK VI . Regular Polygons , and the Area of the Circle . . . . . . 83 . . . . . . .
. 11 % SOLID GEOMETRY . BOOK VIL Planes and Solid Angles . . . . . . BOOK VIII
.
Σελίδα 18
PROPOSITION VIII . THEOREM . Any side of a triangle is less than the sum of the
other two A Let ABC be a triangle ; any one of its sides is less than the sum of the
other two , viz . : the side AB is less than the sum of AC and BC ; BC is less than ...
PROPOSITION VIII . THEOREM . Any side of a triangle is less than the sum of the
other two A Let ABC be a triangle ; any one of its sides is less than the sum of the
other two , viz . : the side AB is less than the sum of AC and BC ; BC is less than ...
Σελίδα 19
PROPOSIT ' ON IX . THEOREM . If , from a point withir a triangle , two straight
lines are drawn to the extremities of either side , their sum will be less han the
sum of the other two sides of the triangle . Produce , because one p . VIII . ) , the d
ED .
PROPOSIT ' ON IX . THEOREM . If , from a point withir a triangle , two straight
lines are drawn to the extremities of either side , their sum will be less han the
sum of the other two sides of the triangle . Produce , because one p . VIII . ) , the d
ED .
Σελίδα 21
But AC is less than the sum of AD and DC ( Prop . VIII . ) ; it is , therefore , less
than AB . Conversely , if the side AB is greater than the side AC , then will the
angle ACB be greater than the angle ABC . For if ACB is not greater than ABC , it
must ...
But AC is less than the sum of AD and DC ( Prop . VIII . ) ; it is , therefore , less
than AB . Conversely , if the side AB is greater than the side AC , then will the
angle ACB be greater than the angle ABC . For if ACB is not greater than ABC , it
must ...
Σελίδα 24
VIII . ) ; hence AB , the half of ABF , is shorter than AC , the half of ACF . Therefore
, the perpendicular AB is shorter than any oblique line , AC . Secondly . Let AC
and AE be two oblique lines which meet the line DE at equal distances from the ...
VIII . ) ; hence AB , the half of ABF , is shorter than AC , the half of ACF . Therefore
, the perpendicular AB is shorter than any oblique line , AC . Secondly . Let AC
and AE be two oblique lines which meet the line DE at equal distances from the ...
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Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle ACB angle BAC base bisected called chord circle circumference coincide College common cone consequently construct contained convex surface curve described diagonals diameter difference distance divided draw drawn ellipse equal equivalent extremities faces fall figure foci formed four frustum given greater half hence hyperbola included inscribed intersect join less Loomis major axis manner Mathematics mean measured meet multiplied opposite ordinate parallel parallelogram parallelopiped pass perpendicular plane plane MN polygon prism PROBLEM Professor Prop proportional PROPOSITION proved pyramid radii radius ratio reason rectangle regular represent right angles Scholium segment sides similar solid sphere spherical square straight line tangent THEOREM third triangle ABC vertex vertices VIII whole
Δημοφιλή αποσπάσματα
Σελίδα 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 17 - If two triangles have two sides, and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal, their third sides will be equal, and their other angles will be equal, each to each.
Σελίδα 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Σελίδα 63 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the' rectangle contained by the parts.
Σελίδα 18 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Σελίδα 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Σελίδα 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Σελίδα 15 - Wherefore, when a straight line, &c. QED PROP. XIV. THEOR. If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Σελίδα 44 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Πληροφορίες βιβλιογραφίας
| Τίτλος | Elements of Geometry and Conic Sections |
| Συγγραφέας | Elias Loomis |
| Έκδοση | 15 |
| Εκδότης | Harper, 1858 |
| Πρωτότυπο από | η Δημόσια Βιβλιοθήκη της Νέας Υόρκης |
| Ψηφιοποιήθηκε στις | 22 Ιουν. 2006 |
| Μέγεθος | 234 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |