Euclid's plane geometry, practically applied; book i, with explanatory notes, by H. Green1863 |
Inni boken
Resultat 1-5 av 7
Side 3
... truths of Geometry , and of having produced a work , which , after the test of above twenty centuries , seems destined to remain the Standard Geometry for ages to come . Euclid's work comprises thirteen books , of which the first four ...
... truths of Geometry , and of having produced a work , which , after the test of above twenty centuries , seems destined to remain the Standard Geometry for ages to come . Euclid's work comprises thirteen books , of which the first four ...
Side 4
... truths and facts ; -I have already proved them and accepted them as principles of Geometrical Reasoning ; and they are now given me that I may arrive at other truths . By using them , can I not demonstrate the inference or conclusion of ...
... truths and facts ; -I have already proved them and accepted them as principles of Geometrical Reasoning ; and they are now given me that I may arrive at other truths . By using them , can I not demonstrate the inference or conclusion of ...
Side 6
... truth , which does not need demonstration ; -it is worthy of credit as soon as stated . A Proposition ( from proponere , to put forth ) , is something proposed to be done , as a problem ; or to be proved , as a theorem . A Problem ...
... truth , which does not need demonstration ; -it is worthy of credit as soon as stated . A Proposition ( from proponere , to put forth ) , is something proposed to be done , as a problem ; or to be proved , as a theorem . A Problem ...
Side 8
... truth ; " the line AC equals the line AB , and the line BC also equals the same line AB , " - this is another truth ; and from the two things thus declared to be true , there is made the unavoidable inference , therefore the two lines ...
... truth ; " the line AC equals the line AB , and the line BC also equals the same line AB , " - this is another truth ; and from the two things thus declared to be true , there is made the unavoidable inference , therefore the two lines ...
Side 9
... truth depends , and the truth itself ; or , as Whately in his Elements of Logic , p . 52 , defines a Syllogism , it is " an argument so expressed , that the conclusiveness of it is manifest from the mere force of the expression , i.e. ...
... truth depends , and the truth itself ; or , as Whately in his Elements of Logic , p . 52 , defines a Syllogism , it is " an argument so expressed , that the conclusiveness of it is manifest from the mere force of the expression , i.e. ...
Vanlige uttrykk og setninger
AB² ABCD adjacent angles altitude angle equal angular point Axiom base BC bisected centre circle circumference coincide CON.-Pst Conc construct Deansgate diagonal diameter divided drawn equal bases equal sides equal triangles equil Euclid exterior angle four rt given line given point given st hypotenuse inference interior angles intersect JOHN HEYWOOD join Let the st line BC line CD measure meet miles opposite angles parallel parallelogram perpendicular Plane Geometry produced PROP proposition proved Quæs rectangle rectil rectilineal angle rectilineal figure right angles Scale of Equal side AC sides and angles square straight line surface Syene Theodolite theorem thing vertex Wherefore
Populære avsnitt
Side 36 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Side 17 - 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...
Side 17 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.
Side 41 - We assume that but one straight line can be drawn through a given point parallel to a given straight line.
Side 13 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 16 - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 54 - 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.
Side 21 - If two angles of a triangle be equal to one another, the sides also which subtend, or are opposite to, the equal angles, shall be equal to one another.
Side 22 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base, equal to one another, and likewise those which are terminated in the other extremity.
Side 12 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.