Elements of Geometry and Conic SectionsHarper, 1849 - 226 Seiten |
Im Buch
Ergebnisse 1-5 von 21
Seite 32
... A B C D Draw the diagonal BC ; then , because AB is parallel to CD , and BC meets them , the alternate angles ABC , BCD are equal to each other ( Prop . XXIII . ) . Also , because AC is parallel to BD , and BC meets them , the alternate ...
... A B C D Draw the diagonal BC ; then , because AB is parallel to CD , and BC meets them , the alternate angles ABC , BCD are equal to each other ( Prop . XXIII . ) . Also , because AC is parallel to BD , and BC meets them , the alternate ...
Seite 58
... ABCD , ABEF be placed so that their equal bases shall coin- C F ED F C E cide with each other . Let AB be the common A B A B base ; and , since the two parallelograms are supposed to have the same altitude , their upper bases , DC , FE ...
... ABCD , ABEF be placed so that their equal bases shall coin- C F ED F C E cide with each other . Let AB be the common A B A B base ; and , since the two parallelograms are supposed to have the same altitude , their upper bases , DC , FE ...
Seite 59
... ABCD will contain seven partial rectangles , while AEFD will contain four ; therefore the rectangle ABCD is to the rectangle AEFD as 7 to 4 , or as AB to AE . The same rea- soning is applicable to any other ratio than that of 7 to 4 ...
... ABCD will contain seven partial rectangles , while AEFD will contain four ; therefore the rectangle ABCD is to the rectangle AEFD as 7 to 4 , or as AB to AE . The same rea- soning is applicable to any other ratio than that of 7 to 4 ...
Seite 60
... ABCD : AHID :: AB : AH . But , by hypothesis , we have ABCD : AEFD :: AB : AG . FI C EHG B In these two proportions the antecedents are equal ; there- fore the consequents are proportional ( Prop . IV . , Cor . , B. II . ) , and we have ...
... ABCD : AHID :: AB : AH . But , by hypothesis , we have ABCD : AEFD :: AB : AG . FI C EHG B In these two proportions the antecedents are equal ; there- fore the consequents are proportional ( Prop . IV . , Cor . , B. II . ) , and we have ...
Seite 61
... ABCD be a parallelogram , AF its F D altitude , and AB its base ; then is its sur- face measured by the product of AB by AF . For , upon the base AB , construct a rectangle having the altitude AF ; the par- allelogram ABCD is equivalent ...
... ABCD be a parallelogram , AF its F D altitude , and AB its base ; then is its sur- face measured by the product of AB by AF . For , upon the base AB , construct a rectangle having the altitude AF ; the par- allelogram ABCD is equivalent ...
Andere Ausgaben - Alle anzeigen
ELEMENTS OF GEOMETRY & CONIC S Elias 1811-1889 Loomis,Making of America Project Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
75 cents ABCD AC is equal allel altitude angle ABC angle ACB angle BAC Anthon's base BCDEF bisected chord circle circumference cone contained convex surface curve described diameter dicular draw drawn ellipse equal angles equal to AC equally distant equiangular equivalent exterior angle foci four right angles frustum greater Hence Prop hyperbola inscribed intersection join latus rectum Let ABC lines AC major axis mean proportional measured by half meet Muslin number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN principal vertex prism PROPOSITION pyramid radii radius ratio rectangle regular polygon right angles Prop Scholium segment Sheep extra side AC similar 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 27 - VIf two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the...
Seite 11 - A rhombus, is that which has all its sides equal, but its angles are not 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 15 - 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 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.
Seite 148 - I.), that every section of a sphere made by a plane is a circle.