A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford |
Dentro del libro
Página 42
If BA is greater than AC , cut off AE = AC , and show that BE the difference of AB and AC - is less than the third side BC . 3. The four sides of a quadrilateral are together greater than its two diagonals . PROPOSITION 21. THEOREM .
If BA is greater than AC , cut off AE = AC , and show that BE the difference of AB and AC - is less than the third side BC . 3. The four sides of a quadrilateral are together greater than its two diagonals . PROPOSITION 21. THEOREM .
Página 52
And it should be noticed that there is this difference between them : the angle ACB opposite AB in the one triangle is acute ( for DCB is an isosceles triangle ) , while ADB , the angle in the other triangle opposite to AB , is obtuse .
And it should be noticed that there is this difference between them : the angle ACB opposite AB in the one triangle is acute ( for DCB is an isosceles triangle ) , while ADB , the angle in the other triangle opposite to AB , is obtuse .
Página 64
Q.E.D. In the phrase the whole or remainder , which occurs in the demonstration , the whole refers to the left - hand figure , where AE is the sum of AD and DE , and the remainder to the right - hand figure , where AE is the difference ...
Q.E.D. In the phrase the whole or remainder , which occurs in the demonstration , the whole refers to the left - hand figure , where AE is the sum of AD and DE , and the remainder to the right - hand figure , where AE is the difference ...
Página 78
Q.E.D. Ex . 1. Shew that if the squares on BA and AC are less than the square on BC the angle BAC is acute ; but if greater than BAC is obtuse . 2. Make a square equal to the difference of two given squares . BOOK II . INTRODUCTION .
Q.E.D. Ex . 1. Shew that if the squares on BA and AC are less than the square on BC the angle BAC is acute ; but if greater than BAC is obtuse . 2. Make a square equal to the difference of two given squares . BOOK II . INTRODUCTION .
Página 88
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 difference of their squares . 1. Let AC .
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 difference of their squares . 1. Let AC .
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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
ABCD AC is equal alternate angles angle ABC angle ACB angle BAC angle BCD angle EDF angle equal apply axioms base BC bisect BOOK called centre circle coincide common Const construction definitions demonstration describe diagonals diameter difference divided double draw equal sides equilateral triangle Euclid exercise exterior angle fall figure fore geometry given point given rectilineal given straight line gnomon greater Hence isosceles triangle join length less Let ABC meet method namely opposite angle opposite sides parallel parallel to CD parallelogram perpendicular PROBLEM produced prop PROPOSITION proved quadrilateral reason rectangle contained rectilineal figure remainder result right angles side BC sides square on AC Take THEOREM things triangle ABC true truths twice the rectangle unequal units whole
Información bibliográfica
| Título | A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford |
| Autor | Euclides |
| Editor | Charles MANSFORD |
| Publicado | 1874 |
| Procedencia del original | Biblioteca Británica |
| Digitalizado | 27 Nov. 2020 |
| Exportar cita | BiBTeX EndNote RefMan |