A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |
Inni boken
Resultat 1-5 av 10
Side 6
... length without breadth , " and it is this mental conception , and not our imperfect representations of it on paper , which Euclid invariably has in view when he uses the word ' line . ' Having thus conceived of a line , we can fix our ...
... length without breadth , " and it is this mental conception , and not our imperfect representations of it on paper , which Euclid invariably has in view when he uses the word ' line . ' Having thus conceived of a line , we can fix our ...
Side 8
... length . 2. A pair of compasses which open to any extent but close immediately they are taken from the paper . It will be seen that neither of these instruments can be used to transfer distances , and also that all con- structions must ...
... length . 2. A pair of compasses which open to any extent but close immediately they are taken from the paper . It will be seen that neither of these instruments can be used to transfer distances , and also that all con- structions must ...
Side 10
... length , and in such a form as to show the truth of the reasoning in the most con- vincing way . Such a syllogism generally takes the following form , which may therefore be regarded as the pattern of all geometrical reasoning . 1. All ...
... length , and in such a form as to show the truth of the reasoning in the most con- vincing way . Such a syllogism generally takes the following form , which may therefore be regarded as the pattern of all geometrical reasoning . 1. All ...
Side 13
... length without breadth . 3. The extremities of a line are points . 4. A straight line is that which lies evenly between its extreme points . 5. A superficies is that which has only length and breadth . 6. The extremities of a ...
... length without breadth . 3. The extremities of a line are points . 4. A straight line is that which lies evenly between its extreme points . 5. A superficies is that which has only length and breadth . 6. The extremities of a ...
Side 17
... That a terminated straight line may be produced to any length in a straight line . 3. And that a circle may be described from any centre , at any distance from that centre . AXIOMS . 1. Things which are equal to the same POSTULATES . 17.
... That a terminated straight line may be produced to any length in a straight line . 3. And that a circle may be described from any centre , at any distance from that centre . AXIOMS . 1. Things which are equal to the same POSTULATES . 17.
Andre utgaver - Vis alle
A School Euclid. Being Books I. & II. of Euclid's Elements, with Notes ... Euclid,Charles Mansford Uten tilgangsbegrensning - 1875 |
A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C ... Euclides Uten tilgangsbegrensning - 1874 |
A School Euclid, Being Books I. & II. of Euclid's Elements, with Notes by C ... Euclides Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
ABCD AC is equal angle ABC angle ACB angle BAC 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 drawn equal sides equal to AC 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
Populære avsnitt
Side 90 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part.
Side 28 - If two triangles have two sides of the one equal to two sides of the...
Side 41 - Any two sides of a triangle are together greater than the third side.
Side 57 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are equal to two right angles.
Side 72 - To describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle. Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.
Side 75 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Side 89 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced...
Side 55 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Side 28 - A two triangles, having the two sides AB, AC, equal to the two sides \ DE, DF, each to each, viz: AB to DE, and AC to DF; and also the base BC equal to the base EF.
Side 69 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.