A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |
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Página 81
... units in AD , i.e. , 3. And the number of columns similar to AF is the same as the number of linear units in AB , which is 4. Therefore we have 3 square units repeated 4 times , and the whole figure consequently contains 3 x 4 or 12 square ...
... units in AD , i.e. , 3. And the number of columns similar to AF is the same as the number of linear units in AB , which is 4. Therefore we have 3 square units repeated 4 times , and the whole figure consequently contains 3 x 4 or 12 square ...
Página 88
... units and CD n units , then AD = m + n , and BD = m - n . But ( m + n ) ( m - n ) = m2 — n2 by multiplication , Hence the corresponding proposition in arithmetic is , The product of the sum and difference of two numbers is equal to the ...
... units and CD n units , then AD = m + n , and BD = m - n . But ( m + n ) ( m - n ) = m2 — n2 by multiplication , Hence the corresponding proposition in arithmetic is , The product of the sum and difference of two numbers is equal to the ...
Página 93
... units and BC b lineal units , shew that this proposition may be expressed in symbols , thus : ( a + b ) - ( a - b ) 2 = 4ab . If AB and BC be considered as two lines , AD is their sum and AC their difference . Therefore four times the ...
... units and BC b lineal units , shew that this proposition may be expressed in symbols , thus : ( a + b ) - ( a - b ) 2 = 4ab . If AB and BC be considered as two lines , AD is their sum and AC their difference . Therefore four times the ...
Página 97
... units , and CD n such units , shew that this proposition may be thus stated , ( m + n ) 2 + ( m − n ) 2 = 2m2 + 2n2 . and prove that the equation is true . PROPOSITION 11. PROBLEM . To divide a given straight line into two parts , so ...
... units , and CD n such units , shew that this proposition may be thus stated , ( m + n ) 2 + ( m − n ) 2 = 2m2 + 2n2 . and prove that the equation is true . PROPOSITION 11. PROBLEM . To divide a given straight line into two parts , so ...
Página 99
... units and CA 8 units , shew that BA will contain very nearly 12 units . PROPOSITION 13. THEOREM . In every triangle , the square BOOK II . 12 . 99.
... units and CA 8 units , shew that BA will contain very nearly 12 units . PROPOSITION 13. THEOREM . In every triangle , the square BOOK II . 12 . 99.
Otras ediciones - Ver todas
A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ... Euclides Vista completa - 1874 |
A School Euclid, Being Books I. & II. of Euclid's Elements, with Notes by C ... Euclides Sin vista previa disponible - 2015 |
Términos y frases comunes
AC is equal adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal angles are equal angles CBA axioms base BC BC is equal bisect centre circle coincide Const diagonals diameter double equal sides equal to BC equal to twice equilateral triangle Euclid exterior angle fore four right angles given point given rectilineal angle given straight line gnomon half a right hypotenuse interior and opposite isosceles triangle join Let ABC Let the straight obtuse opposite angle opposite sides parallel to CD parallelogram parallelogram ABCD perpendicular produced prop PROPOSITION quadrilateral rectangle AC rectangle contained remaining angle rhombus right angles right-angled triangle shew side BC sides equal square described square on AC THEOREM third angle triangle ABC triangle DEF truths twice the rectangle unequal