Elements of the Geometry of Planes and Solids: With Four PlatesThe author, 1828 - 159 sider |
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Side 8
... less , which being proved to lead to a contradiction of themselves are inadmissible , and therefore the equality alone admissible . It may be proper here to state those axioms which are ge- neral to all Mathematics , as they relate to ...
... less , which being proved to lead to a contradiction of themselves are inadmissible , and therefore the equality alone admissible . It may be proper here to state those axioms which are ge- neral to all Mathematics , as they relate to ...
Side 12
... less than a right angle . In figure 1 , the angle EAD , is an acute angle . 10 Figure , is any space terminated . ( So figure 2 to 8 are figures in that sense , as they inclose or terminate a space . ) 11. A circle , is a plane figure ...
... less than a right angle . In figure 1 , the angle EAD , is an acute angle . 10 Figure , is any space terminated . ( So figure 2 to 8 are figures in that sense , as they inclose or terminate a space . ) 11. A circle , is a plane figure ...
Side 26
... less than two right angles ; because they are less than the sum of the angles made by lines meeting in one point on the same side of one straight line . Scholium 2. A triangle cannot have more than one angle , a right angle or an obtuse ...
... less than two right angles ; because they are less than the sum of the angles made by lines meeting in one point on the same side of one straight line . Scholium 2. A triangle cannot have more than one angle , a right angle or an obtuse ...
Side 27
... less the less ; as was to be demonstrated . § 18. THEOREM . To the greater angle of a triangle the greater side is opposite . APPLIC . Let the angle at B , in the triangle ABC , ( fig . 6 , ) be greater than the angle C , then will the ...
... less the less ; as was to be demonstrated . § 18. THEOREM . To the greater angle of a triangle the greater side is opposite . APPLIC . Let the angle at B , in the triangle ABC , ( fig . 6 , ) be greater than the angle C , then will the ...
Side 32
... less than two right angles ; but by the sup- position these two angles are equal to two right angles , which is again contradictory ; therefore , the protracted straight lines AB , and CD , do not meet ; they are , therefore , parallel ...
... less than two right angles ; but by the sup- position these two angles are equal to two right angles , which is again contradictory ; therefore , the protracted straight lines AB , and CD , do not meet ; they are , therefore , parallel ...
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Elements of the Geometry of Planes and Solids: With Four Plates Ferdinand Rudolph Hassler Uten tilgangsbegrensning - 1828 |
Elements of the Geometry of Planes and Solids: With Four Plates (Classic ... F. R. Hassler Ingen forhåndsvisning tilgjengelig - 2018 |
Vanlige uttrykk og setninger
ABCD angle equal angle G angles opposite angular point APPLIC base and altitude bisect centre chord circumference circumscribed circle common intersection cone Corol cutting line cylinder Demonstr describe determine diagonal diameter draw drawn equal angles equal base equal sides equiangular equilateral triangle four right angles frustum given angle given circle given lines given point given straight line given triangle gles greater inner angles inscribed join line BC opposite angles parallel planes parallelepiped parallelogram perpendicular plane angles Plane Geometry point of intersection prisms PROBLEM Proof proportional protracted pyramid quadrilateral figure radii radius ratio rectilineal figure regular poligon Scholium segment side AC similar similar triangles six right solid angle solid content sphere square subtended supposition surface tangent thence THEOREM third plane third side three plane three sides triangle ABC triangular vertex
Populære avsnitt
Side 44 - IN right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar and similarly described figures upon the sides containing the right angle...
Side 20 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Side 11 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Side 2 - BBOWN, of the said district, hath deposited in this office the title of a book, the right whereof he claims as author, in the words following, to wit : " Sertorius : or, the Roman Patriot.
Side 36 - 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.
Side 119 - If a solid angle be contained by three plane angles, any two of them are together greater than the third. Let the solid angle at A be contained by the three plane angles BAC, CAD, DAB : any two of them shall be together greater than the third.
Side 61 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle. Let AB be the given straight line, and...
Side 113 - If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane.
Side 29 - EBF, there are two angles in the one equal to two angles in the other, each to each ; and the side EF, which is opposite to one of the equal angles in each, is common to both ; therefore the other sides are equal ; (I.
Side 16 - E the centre of the circle, and join EA, EB. Then, because AF is equal to FB, and FE common to the two triangles AFE, BFE, there are two sides in the one, equal to two sides in the other, and the base EA is equal to the base EB; therefore the angle AFE is equal...