Elements of the Geometry of Planes and Solids: With Four PlatesThe author, 1828 - 159 Seiten |
Im Buch
Ergebnisse 1-5 von 21
Seite 15
... smaller . APPLICATION . Let AB , be a given straight line larger than CD , it is required to cut off from AB , a line equal to CD . ( Fig . 12. ) Solution . From the point A , lay off the straight line AE , in any direction and equal to ...
... smaller . APPLICATION . Let AB , be a given straight line larger than CD , it is required to cut off from AB , a line equal to CD . ( Fig . 12. ) Solution . From the point A , lay off the straight line AE , in any direction and equal to ...
Seite 16
... smaller than AB , the circle described with AE , or AF , must cut it , therefore the AE , is cut off from the AB , equal to CD , as was required . $ 4. THEOREM . If two triangles have two sides in the one equal to two sides in the other ...
... smaller than AB , the circle described with AE , or AF , must cut it , therefore the AE , is cut off from the AB , equal to CD , as was required . $ 4. THEOREM . If two triangles have two sides in the one equal to two sides in the other ...
Seite 18
... smaller equal to the greater , which is impos- sible ; therefore , the sides AB , and AC , are not unequal ; that is , if two angles in a triangle are equal , the sides opposite to these angles are also equal . Corol . Every equiangular ...
... smaller equal to the greater , which is impos- sible ; therefore , the sides AB , and AC , are not unequal ; that is , if two angles in a triangle are equal , the sides opposite to these angles are also equal . Corol . Every equiangular ...
Seite 24
... smaller than the one right angle ; that is , the one obtuse , the other acute . Corol . 2. Any number of lines meeting another line on the same side , and at the same point , always make their sum equal to- gether to two right angles ...
... smaller than the one right angle ; that is , the one obtuse , the other acute . Corol . 2. Any number of lines meeting another line on the same side , and at the same point , always make their sum equal to- gether to two right angles ...
Seite 27
... smaller line , join CD ; the angle ACD , will be equal to the angle ADC , because AC = AD ; the angle ADC , is outward angle to the triangle DBC ; therefore , greater than the angle CBD , or CBA , one of the inward opposite angles of ...
... smaller line , join CD ; the angle ACD , will be equal to the angle ADC , because AC = AD ; the angle ADC , is outward angle to the triangle DBC ; therefore , greater than the angle CBD , or CBA , one of the inward opposite angles of ...
Andere Ausgaben - Alle anzeigen
Elements of the Geometry of Planes and Solids: With Four Plates (Classic ... F. R. Hassler Keine Leseprobe verfügbar - 2018 |
Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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...
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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...
Seite 113 - If one of two parallel lines is perpendicular to a plane, the other is also perpendicular to the plane.
Seite 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.
Seite 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...