The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate |
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Seite 6
Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . ... to AB ; and because the point B is the centre of the circle ACE , BC is equal to BA : But it has been proved that ...
Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . ... to AB ; and because the point B is the centre of the circle ACE , BC is equal to BA : But it has been proved that ...
Seite 7
the same are equal to one another ( Axiom 1. ) ; therefore CA is equal to CB ; wherefore CA , AB , BC are equal to one another ; and the triangle ABC is therefore equilateral , and it is described upon the given straight line AB .
the same are equal to one another ( Axiom 1. ) ; therefore CA is equal to CB ; wherefore CA , AB , BC are equal to one another ; and the triangle ABC is therefore equilateral , and it is described upon the given straight line AB .
Seite 8
whence AE and c are each of them equal to AD ; wherefore the straight line AE is equal to c ( Ax . 1. ) ... BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other ...
whence AE and c are each of them equal to AD ; wherefore the straight line AE is equal to c ( Ax . 1. ) ... BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other ...
Seite 9
angles contained by those sides equal to one another , their bases shall likewise be equal , and the triangles be ... FC are equal to the two CG , GB , each to each ; and the angle BFC is equal to the angle CGB , and the base BC is ...
angles contained by those sides equal to one another , their bases shall likewise be equal , and the triangles be ... FC are equal to the two CG , GB , each to each ; and the angle BFC is equal to the angle CGB , and the base BC is ...
Seite 10
off DB equal to AC , the less , and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to ...
off DB equal to AC , the less , and join DC ; therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal to ...
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The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Keine Leseprobe verfügbar - 2014 |
The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Keine Leseprobe verfügbar - 2014 |
Häufige Begriffe und Wortgruppen
ABCD adjacent angle ABC angle ACB angle BAC angle equal base BC BC is equal bisect centre circle ABC circumference coincide common construct demonstrated describe diameter divided double draw equal angles equal to FB equilateral exterior angle extremity figure fore four given point given straight line gnomon greater impossible interior isosceles triangle join less Let ABC Let the straight likewise line be drawn manner meet opposite angles opposite sides parallel parallelogram pass perpendicular PROB produced PROP rectangle contained remaining angle right angles segment semicircle shown side BC sides square of AC straight line AC Take taken THEOR third touch touches the circle triangle ABC twice the rectangle vertex wherefore whole
Beliebte Passagen
Seite 6 - 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...
Seite 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 20 - If two triangles have two sides of the one equal to two sides of the...
Seite 30 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.
Seite 17 - Any two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles.
Seite 84 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square of the line which meets it, the line which meets it shall touch the circle.
Seite 82 - 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.
Seite 11 - 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.
Seite 19 - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third, (i.
Seite 7 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Bibliografische Informationen
| Titel | The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate |
| Autoren | Euclid, Thomas Tate |
| Herausgeber | Thomas Tate |
| Verlag | Longman, Brown, Green, and Longmans, 1849 |
| Original von | Oxford University |
| Digitalisiert | 16. Okt. 2006 |
| Länge | 108 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |