Elements of Geometry: With, Practical ApplicationsD. Appleton and Company, 1850 - 320 σελίδες |
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Αποτελέσματα 1 - 5 από τα 22.
Σελίδα 181
... planes is the line in which they meet to cut each other . 2. A line is perpendicular to a plane , when it is per ... parallel to a plane , when , if both are pro- duced to any distance , they do not meet ; and , conversely , the plane is then ...
... planes is the line in which they meet to cut each other . 2. A line is perpendicular to a plane , when it is per ... parallel to a plane , when , if both are pro- duced to any distance , they do not meet ; and , conversely , the plane is then ...
Σελίδα 189
... parallel to each other . When the three lines are in the same plane , the case corresponds with Book I , Prop . xxi ... planes ; but AB cannot meet CD , since they are parallel ; hence it will not meet the plane MN ; therefore ( Def . 5 ...
... parallel to each other . When the three lines are in the same plane , the case corresponds with Book I , Prop . xxi ... planes ; but AB cannot meet CD , since they are parallel ; hence it will not meet the plane MN ; therefore ( Def . 5 ...
Σελίδα 190
... line , which is im- possible ; hence the planes MN , PQ cannot meet each other , and consequently they are parallel . PROPOSITION X. THEOREM . The intersections of two parallel planes with a third plane are parallel . Let the two parallel ...
... line , which is im- possible ; hence the planes MN , PQ cannot meet each other , and consequently they are parallel . PROPOSITION X. THEOREM . The intersections of two parallel planes with a third plane are parallel . Let the two parallel ...
Σελίδα 191
... planes would not be parallel . PROPOSITION XI . THEOREM . A line which is perpendicular to one of two parallel planes , is perpendicular to the other also . Let the two planes MN and PQ be parallel ; then if the line AB is perpendicular to ...
... planes would not be parallel . PROPOSITION XI . THEOREM . A line which is perpendicular to one of two parallel planes , is perpendicular to the other also . Let the two planes MN and PQ be parallel ; then if the line AB is perpendicular to ...
Σελίδα 192
With, Practical Applications George Roberts Perkins. Let EG , FH be two parallel lines included between the two parallel planes MN , PQ ; then will these lines be equal . Through the parallels EG , FH , draw the plane EGHF to meet the ...
With, Practical Applications George Roberts Perkins. Let EG , FH be two parallel lines included between the two parallel planes MN , PQ ; then will these lines be equal . Through the parallels EG , FH , draw the plane EGHF to meet the ...
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Elements of Geometry With Practical Applications George R Perkins Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2023 |
Συχνά εμφανιζόμενοι όροι και φράσεις
a+b+c altitude angle ABC angle BAC angle BCD bisect centre chord circ circular sector circumference circumscribed polygon coincide cone consequently convex surface cylinder denote diagonal diameter dicular distance draw equal and parallel equiangular equilateral triangle equivalent exterior angle figure formed given line greater half the arc hypothenuse inscribed circle intersection isosceles join less Let ABC line AC line CD lines drawn measured by half meet multiplied number of sides parallel planes parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN point G prism PROBLEM produced Prop PROPOSITION pyramid radii radius rectangle regular polygon respectively equal right-angled triangle Sabc Schol Scholium scribed semicircle semicircumference side AC similar similar triangles solid angle sphere spherical triangle square straight line suppose tangent THEOREM three sides triangle ABC triangular prism vertex VIII
Δημοφιλή αποσπάσματα
Σελίδα 231 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Σελίδα 147 - PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given triangle : it is required to inscribe a circle in the triangle ABC.
Σελίδα 17 - 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.
Σελίδα 28 - If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other...
Σελίδα 233 - The volume of a cylinder is equal to the product of its base by its altitude. Let the volume of the cylinder be denoted by V, its base by B, and its altitude by H.
Σελίδα 276 - THEOREM. Two triangles on the same sphere, or on equal spheres, are equal in all their parts, when they have each an equal angle included between equal sides. Suppose the side...
Σελίδα 120 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Σελίδα 18 - If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another.
Σελίδα 232 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Σελίδα 96 - Similar figures, are those that have all the angles of the one equal to all the angles of the other, each to each, and the sides about the equal angles proportional.