Elements of Geometry and Conic SectionsHarper, 1858 - 234 Seiten |
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Seite 37
... means . Of four proportional quantities , the last is called a fourth proportional to the other three , taken in order ... mean propor- tional between the other two . Def . 4. Two magnitudes are said to be equimultiples of two others ...
... means . Of four proportional quantities , the last is called a fourth proportional to the other three , taken in order ... mean propor- tional between the other two . Def . 4. Two magnitudes are said to be equimultiples of two others ...
Seite 38
... means . It has been shown that the ratio of two magnitudes , wheth- er they are lines , surfaces , or solids , is the ... mean . Thus , if A : B :: B : C ; then , by the proposition , AXC - BXB , which is equal to B ' . PROPOSITION II ...
... means . It has been shown that the ratio of two magnitudes , wheth- er they are lines , surfaces , or solids , is the ... mean . Thus , if A : B :: B : C ; then , by the proposition , AXC - BXB , which is equal to B ' . PROPOSITION II ...
Seite 39
... means of a proportion . Thus , suppose we have AxD - BXC ; then will A : B :: C : D. For , since AxD = BxC , dividing each of these equals by D ( Axiom 2 ) , we have BXC A : D Dividing each of these last equals by B , we obtain A C. B ...
... means of a proportion . Thus , suppose we have AxD - BXC ; then will A : B :: C : D. For , since AxD = BxC , dividing each of these equals by D ( Axiom 2 ) , we have BXC A : D Dividing each of these last equals by B , we obtain A C. B ...
Seite 74
... mean proportional between the segments of the hypothenuse . 3d . Each of the sides is a mean proportional between the hy- pothenuse and its segment adjacent to that side . Let ABC be a right - angled triangle , hav- ing the right angle ...
... mean proportional between the segments of the hypothenuse . 3d . Each of the sides is a mean proportional between the hy- pothenuse and its segment adjacent to that side . Let ABC be a right - angled triangle , hav- ing the right angle ...
Seite 75
Elias Loomis. the perpendicular AD is a mean proportional between BD and DC , the two segments of the diameter ; that is , AD ' BDX DC . = PROPOSITION XXIII . THEOREM . Two triangles , having an angle in the one equal to an angle in the ...
Elias Loomis. the perpendicular AD is a mean proportional between BD and DC , the two segments of the diameter ; that is , AD ' BDX DC . = PROPOSITION XXIII . THEOREM . Two triangles , having an angle in the one equal to an angle in the ...
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Häufige Begriffe und Wortgruppen
ABCD AC is equal allel altitude angle ABC angle ACB angle BAC base BCDEF bisected chord circle circumference cone convex surface curve described diagonals diameter draw ellipse equal angles equal to AC equally distant equiangular equilateral equivalent exterior angle foci four right angles frustum given angle given point greater hyperbola hypothenuse inscribed intersect join latus rectum Let ABC lines AC Loomis major axis mean proportional measured by half meet number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN prism Professor of Mathematics PROPOSITION pyramid radii radius ratio rectangle regular polygon right angles Prop Scholium segment side AC similar similar triangles slant height solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Beliebte Passagen
Seite 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Seite 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.
Seite 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Seite 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.
Seite 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.