 | Euclides - 1846 - 292 sider
...in that plane, and therefore CAE is a right angle : In like manner, BAE is a right angle; therefore the angle CAE is equal to the angle BAE, and they are in the same plane — which is impossible. Also, from a point above a plane, there can be drawn but one... | |
 | Euclides - 1855 - 230 sider
...but DAE, which is in that plane, meets CA; therefore CAE is a right angle: for the same reason, BAE is a right angle; wherefore the angle CAE is equal to the angle BAE (c); and they are in one plane, which is impossible. Also, from a point above a plane, there can be... | |
 | Euclides - 1855 - 270 sider
...right angle. For the same reason, BAE ie a right angle. Wherefore the angle СAE is equal (I. Ax. 11) to the angle BAE ; and they are in one plane, which is impossible (I. Ax. 9). Therefore two perpendiculars cannot be drawn from the same point in a plane, on the same... | |
 | Eucleides - 1860 - 396 sider
...but DAE, which is in that plane, meets CA ; therefore CAE is a right angle : for the same reason, BAE is a right angle ; wherefore the angle CAE is equal to the angle BAE (c) ; and they are in one plane, which is impossible. Also, from a point above a plane, there can be... | |
 | Euclides - 1864 - 448 sider
...but DAE, which is in that plane, meets CA; therefore CAE is a right angle. For the same reason, BAE is a right angle. Wherefore the angle CAE is equal to the angle BAE; (ax. 11.) and they are in one plane, which is impossible. Also, from a point above a plane, there can... | |
 | Euclides - 1865 - 402 sider
...right angle ; therefore the angle CAE must be equal to the angle BAE ; (i. ax. 1 1. ) and they must be in one plane; which is impossible. Also, from a point above a plane, there can be bnt one perpendicular to that plane ; for, if there could be two, they would be parallel to one another,... | |
 | Robert Potts - 1865 - 528 sider
...but DAE, which is in that plane, meets CA ; therefore CAE is a right angle. For the same reason, BAE is a right angle. Wherefore the angle CAE is equal to the angle BAE; (ax. 11.) and they are in one plane, which is impossible. Also, from a point above a plane, there can... | |
 | John Playfair - 1855 - 350 sider
...therefore CA E is a right angle. For the same reason BAE is a right angle. Wherefore the angle CAE is eqnal to the angle BAE ; and they are in one plane, which...impossible. Also, from a point above a plane, there can bo but one perpendicular to that plane ; for if there could be two, they would be parallel (6. 2. Sup.)... | |
 | Robert Potts - 1868 - 434 sider
...but DAE, which is in that plane, meets CA ; therefore CAE is a right angle. For the same reason, BAE is a right angle. Wherefore the angle CAE is equal to the angle BAE; (ax. 11.) and they are in one plane, which is impossible. Also, from a point above a plane, there can... | |
 | Euclides - 1874 - 342 sider
...DE, which is in that plane, meets CA ; therefore 2. CAE is a right angle. For the same reason, BAE is a right angle ; wherefore the angle CAE is equal to the angle BAE (I. Ax. 11), therefore 3. CAE and BAE are in one plane, which is impossible (I. Ag, 9). Therefore two... | |
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CA is at right angles to the given plane, it makes right angles with every straight line meeting it in that plane. But DAE, which is in that plane, meets CA : therefore CAE is a right angle. For the same reason BAE is a right angle. Wherefore the angle... 
