Elements of Geometry: Being Chiefly a Selection from Playfair's GeometryA. Walker, 1829 - 186 Seiten |
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Seite 4
... same kind , else they can- not be compared together , and therefore no judgment of their equality or inequality can be ... equal ratios , it is called a tripli- cate ratio , & c . Thus , if A B C AC = m , and = m , then = m2 , BD that is ...
... same kind , else they can- not be compared together , and therefore no judgment of their equality or inequality can be ... equal ratios , it is called a tripli- cate ratio , & c . Thus , if A B C AC = m , and = m , then = m2 , BD that is ...
Seite 8
... equal to , or less than the second , the third quantity is greater than , equal to , or less than the fourth . = Let A B C : D , then AD : BC ( 26 ) , .. if A be greater than B , then C is greater than D , if A = B , then C = D , and if ...
... equal to , or less than the second , the third quantity is greater than , equal to , or less than the fourth . = Let A B C : D , then AD : BC ( 26 ) , .. if A be greater than B , then C is greater than D , if A = B , then C = D , and if ...
Seite 16
... same way . See Note . ED . 4. Cor . Hence a straight line is the least ... same point , the opening between them is called an angle . ED . 10. An angle is ... ABC is greater than the angle DBC . ED . ELEMENTS OF GEOMETRY . BOOK I. A D 17 B.
... same way . See Note . ED . 4. Cor . Hence a straight line is the least ... same point , the opening between them is called an angle . ED . 10. An angle is ... ABC is greater than the angle DBC . ED . ELEMENTS OF GEOMETRY . BOOK I. A D 17 B.
Seite 17
... ABC , or CBA ; that which is contained by AB , BD , is named the angle ABD ... equal to each other , each of the an- gles is called a right angle ; and the ... equal to one another . For they are formed by straight lines standing ...
... ABC , or CBA ; that which is contained by AB , BD , is named the angle ABD ... equal to each other , each of the an- gles is called a right angle ; and the ... equal to one another . For they are formed by straight lines standing ...
Seite 22
... equal to AB . But things which are equal to the same thing are equal to one another ( 1 Axiom ) ; therefore CA is equal to CB ; wherefore CA , AB , BC are equal to one another ; and they form a triangle ABC ; therefore the triangle ABC ...
... equal to AB . But things which are equal to the same thing are equal to one another ( 1 Axiom ) ; therefore CA is equal to CB ; wherefore CA , AB , BC are equal to one another ; and they form a triangle ABC ; therefore the triangle ABC ...
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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.