Elements of geometry, containing books i. to vi.and portions of books xi. and xii. of Euclid, with exercises and notes, by J.H. Smith |
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Αποτελέσματα 1 - 5 από τα 81.
Σελίδα 1
... a Solid Body . The stone - cutter shapes it , and brings it into that which we call regularity of form ; and then it becomes a ... POINT is that 1 INTRODUCTORY REMARKS ON SOLIDS, SURFACES, LINES, AND POINTS.
... a Solid Body . The stone - cutter shapes it , and brings it into that which we call regularity of form ; and then it becomes a ... POINT is that 1 INTRODUCTORY REMARKS ON SOLIDS, SURFACES, LINES, AND POINTS.
Σελίδα 2
... a visible line without breadth ; but we can reason about lines as if they had no breadth , and this is what Euclid requires us to do . III . The EXTREMITIES of finite LINES are points . A point marks position , as for instance , the place ...
... a visible line without breadth ; but we can reason about lines as if they had no breadth , and this is what Euclid requires us to do . III . The EXTREMITIES of finite LINES are points . A point marks position , as for instance , the place ...
Σελίδα 3
... points which we know from experience . It is , however , to be observed that Geometry requires us to conceive the possibility of the existence of a Surface apart from a Solid body , of a Line apart from a Surface . of a Point apart from a ...
... points which we know from experience . It is , however , to be observed that Geometry requires us to conceive the possibility of the existence of a Surface apart from a Solid body , of a Line apart from a Surface . of a Point apart from a ...
Σελίδα 7
... point . II . That a terminated straight line may be produced to any length in a straight line . III . That a circle ... given line , and whose circumference passes through the other extremity of that line . The restriction is , that the ...
... point . II . That a terminated straight line may be produced to any length in a straight line . III . That a circle ... given line , and whose circumference passes through the other extremity of that line . The restriction is , that the ...
Σελίδα 10
... given straight line . B E Let AB be the given st . line . It is required to describe an equilat . △ on AB . With centre A and distance AB describe BCD . Post . 3 . With centre B and ... a given point to 10 [ Book I. EUCLID'S ELEMENTS .
... given straight line . B E Let AB be the given st . line . It is required to describe an equilat . △ on AB . With centre A and distance AB describe BCD . Post . 3 . With centre B and ... a given point to 10 [ Book I. EUCLID'S ELEMENTS .
Συχνά εμφανιζόμενοι όροι και φράσεις
AB=DE ABCD AC=DF angles equal angular points base BC BC=EF centre chord circumference coincide described diagonals diameter divided draw equal angles equiangular equilateral triangle equimultiples Eucl Euclid exterior angle given circle given line given point given straight line greater than nB Hence hypotenuse inscribed intersect isosceles triangle less Let ABC Let the st lines be drawn magnitudes middle points multiple opposite angles opposite sides parallel parallelogram pentagon perpendicular plane polygon produced Prop prove Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radius ratio rectangle contained reflex angle rhombus right angles segment shew shewn square subtended sum of sqq tangent THEOREM together=two rt trapezium triangle ABC triangles are equal vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 89 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Σελίδα 168 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 7 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 40 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Σελίδα 23 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.
Σελίδα 106 - 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 ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Σελίδα 178 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 46 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...
Σελίδα 285 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 91 - In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.