Elements of Geometry: Being Chiefly a Selection from Playfair's GeometryA. Walker, 1829 - 186 Seiten |
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Seite 70
... described on AB consists of four parts . The first part is the square CK described on BC ; the second is FH or the square on AC , for CF and KH , being parallel to the sides of the square AF , are equal , therefore if the equal parts CG ...
... described on AB consists of four parts . The first part is the square CK described on BC ; the second is FH or the square on AC , for CF and KH , being parallel to the sides of the square AF , are equal , therefore if the equal parts CG ...
Seite 72
... described on half the line . For AD.DB = AC2 CD2 , therefore the rect . AD . DB is always less than AC by CD2 , and constantly increases as DC decreases , till the point D coincide with C , and then AD.DB becomes AC . CB , or AC3 ...
... described on half the line . For AD.DB = AC2 CD2 , therefore the rect . AD . DB is always less than AC by CD2 , and constantly increases as DC decreases , till the point D coincide with C , and then AD.DB becomes AC . CB , or AC3 ...
Seite 73
... described on the hypothenuse is equal to both the squares de- scribed on the other two sides . Let ABC be a right angled triangle , having the right angle ACB , and let the squares AE , FC , CI be described on the three sides AB , AC ...
... described on the hypothenuse is equal to both the squares de- scribed on the other two sides . Let ABC be a right angled triangle , having the right angle ACB , and let the squares AE , FC , CI be described on the three sides AB , AC ...
Seite 74
... described on one of the sides of a right angled triangle is equal to the difference of the squares de- scribed on the hypothenuse and the other side . For AC + BC AB3 . From these equals take BC3 , then AC ABo 2 · BC . ED . COR . 2. If ...
... described on one of the sides of a right angled triangle is equal to the difference of the squares de- scribed on the hypothenuse and the other side . For AC + BC AB3 . From these equals take BC3 , then AC ABo 2 · BC . ED . COR . 2. If ...
Seite 81
... described on the hypothenuse is equal to both the squares des- cribed on the other two sides . If two right angled triangles have two sides of one tria gle equal to two corresponding sides of the other , they are equal in all respects ...
... described on the hypothenuse is equal to both the squares des- cribed on the other two sides . If two right angled triangles have two sides of one tria gle equal to two corresponding sides of the other , they are equal in all respects ...
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Elements of Geometry: Being Chiefly a Selection From Playfair's Geometry John Playfair Keine Leseprobe verfügbar - 2023 |
Elements of Geometry: Being Chiefly a Selection From Playfair's Geometry John Playfair Keine Leseprobe verfügbar - 2023 |
Häufige Begriffe und Wortgruppen
ABC is equal ABCD alternate angles angle ABC angle ACB angle BAC angles AGH angles equal base ABC bases and altitudes bisect centre chord circumference cone Consequently cylinder demonstrations described diagonals diameter divided draw equal angles equal arches equal bases equal circles equal to AC equiangular Euclid's Euclid's Elements exterior angle fore four quantities four right angles geometry given point given straight line gles greater Hence homologous sides intersect KLMN Let ABC meet opposite angles opposite side paral parallel lines parallel to CD parallelogram parallelopipeds perp perpendicular plane polygon prism Prop pyramid Q. E. D. COR Q. E. D. PROPOSITION radius rectangle contained right angled triangle Scholium segments semicircle side AC similar similar triangles solid square straight line &c subtended tangent THEOREM triangle ABC vertex wherefore
Beliebte Passagen
Seite 36 - Any two sides of a triangle are together greater than the third side.
Seite 80 - 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 42 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line...
Seite 30 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.
Seite 20 - LET it be granted that a straight line may be drawn from any one point to any other point.
Seite 38 - Problem. At a given point in a given straight line to make a rectilineal angle equal to a given rectilineal angle.
Seite 113 - Wherefore also the angle BAD is equal to the angle CAD : Therefore the angle BAC is cut into two equal angles by the straight line AD.
Seite 24 - DE ; the point B shall coincide with the point E, because AB is equal to DE; and AB coinciding with DE, AC shall coincide...
Seite 36 - The greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.