Euclid's plane geometry, practically applied; book i, with explanatory notes, by H. Green1863 |
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Página 7
... height ) , of a figure is the perpendicular distance from the side or angle opposite to the base , to the base itself , or to the base produced . A Diagonal ( diagonios , from corner to corner ) , is a line joining two opposite angular ...
... height ) , of a figure is the perpendicular distance from the side or angle opposite to the base , to the base itself , or to the base produced . A Diagonal ( diagonios , from corner to corner ) , is a line joining two opposite angular ...
Página 23
... height BA . The height would also be obtained by making an obser- vation with a quadrant of altitude . PROP . 7. - THEOR . Upon the same base and upon the same side of it there cannot be two triangles that have their sides which are ...
... height BA . The height would also be obtained by making an obser- vation with a quadrant of altitude . PROP . 7. - THEOR . Upon the same base and upon the same side of it there cannot be two triangles that have their sides which are ...
Página 33
... triangle the perpendicular of which shall be representative of the height of any object . - See " Euclid Practically Applied , " Part I. , Pr . 20 , I. p . 84 . C PROP . 21. - THEOR . If from the ends PROP . 20. - BOOK I. 3333.
... triangle the perpendicular of which shall be representative of the height of any object . - See " Euclid Practically Applied , " Part I. , Pr . 20 , I. p . 84 . C PROP . 21. - THEOR . If from the ends PROP . 20. - BOOK I. 3333.
Página 46
... height of a mountain as CD . Q.E.D. B B D E At station A with a theodolite ascertain the angle CAD , -suppose 45 ° , measure AB 300 feet , and at station B measure the angle CBD , 309 ; and from these data construct the figure required ...
... height of a mountain as CD . Q.E.D. B B D E At station A with a theodolite ascertain the angle CAD , -suppose 45 ° , measure AB 300 feet , and at station B measure the angle CBD , 309 ; and from these data construct the figure required ...
Página 47
... height of a mountain AG , as well as the distance from the base to the foot of the perpendicular , CG . Take a large right - angled triangle , ABD and putting one end at A , let the side DB , by means of a plummet , be brought to the ...
... height of a mountain AG , as well as the distance from the base to the foot of the perpendicular , CG . Take a large right - angled triangle , ABD and putting one end at A , let the side DB , by means of a plummet , be brought to the ...
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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...
Página 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.
Página 41 - We assume that but one straight line can be drawn through a given point parallel to a given straight line.
Página 13 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 16 - LET it be granted that a straight line may be drawn from any one point to any other point.
Página 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.
Página 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.
Página 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.
Página 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.